12th International Conference on the Exact Renormalization Group 2024 (ERG2024)

22 Sept 2024, 19:00 → 27 Sept 2024, 14:30 Europe/Zurich

Maison des Congrès

Fabian Rennecke, Laura Classen (MPI Stuttgart), Luca Zambelli, Nicolo Defenu (ETH Zurich)

The ERG conferences, held every second year, are intended to bring together researchers from different branches of theoretical physics who apply modern functional renormalization group (fRG) methods to describe and understand a variety of physical phenomena. For example, applications include quantum many-body systems, statistical mechanics, particle physics, nuclear physics and quantum theories of gravity. The conference is intended to foster collaboration and scientific exchange both within the growing fRG community and among the various communities working on non-perturbative methods, renormalizationgroup (RG) approaches, and modern developments in field-theoretical methods. To this end, besides providing ample space for a detailed account of the recent developments of the fRG method and its applications, the event will also host plenary review talks on different research directions of topical interest for the contemporary theoretical-physics community.

Registration is open until June 30th. Applicants will be considered on a first come first served basis.

Participants of the conference will be accommodated in different hotels located in Les Diablerets between 5 and 20 minutes by foot from the conference venue. All meals excepted breakfast will be taken together at Hotel les Sources, and covered by the organisers’ funding.

Speakers will have their accommodation in single room covered by the organisers as well. 

Other applicants can request financial support for the accommodation in the registration form by ticking the corresponding box.

As a general rule, no travel expenses will be covered. However, some exceptions might be possible: please contact Nicolò Defenu at ndefenu@phys.ethz.ch  for more information.

-----------------------

BEWARE PHISHING SCAMS regarding accommodation, in particular emails from a "Royal Visit" or "Global Travel Experts" company. 

Do not give your credit card or other personal information to anyone claiming affiliation. No payments need to be made in advance for the conference.

Your main contact for this event remain the organizers or contact@swissmaprs.ch.

-----------------------

HOW TO GET THERE

The easiest way to get to Les Diablerets is by train/bus. From Geneva, Basel or Zurich, you will need to change in Aigle (VD) (you can plan your trip by clicking on SBB CFF). From Aigle to Les Diablerets, there is one train every hour arriving at xx:19.

-----------------------

International Advisory Committee

M. Birse (Manchester), J. P. Blaizot (Saclay), L. Canet (Grenoble, Paris), B. Delamotte (Paris), A. Eichhorn (Odense), T. Kunihiro (Kyoto), D. F. Litim (Sussex), W. Metzner (Stuttgart), N. Ohta (NCU Taiwan, Osaka), R. Percacci (Trieste), M. Salmhofer (Heidelberg), N. Tetradis (Athens), C. Wetterich (Heidelberg)

Monday 23 September

08:50 → 09:00 Welcome

09:00 → 09:40 Towards an FRG study of many-body localization

Disorder is known to induce a localized phase in a 1D Bose gas at zero temperature. It has been predicted that this insulating phase can survive at low temperatures, but the possible existence of such many-body localized phases in 1D quantum systems is a controversial issue. We discuss the finite-temperature phase diagram of a 1D disordered boson system using bosonization, the replica formalism and FRG. While the derivative expansion indicates that localization effects are still important at non-zero temperatures, it fails at low temperatures and we argue that a final answer regarding the existence of a true many-body localized phase can only be obtained from the BMW approximation.

Speaker: Nicolas Dupuis

erg2024_Dupuis.pdf

09:40 → 10:20 Hydrodynamic attractors for strongly correlated fermions

In heavy ion collisions, hydrodynamic attractors can describe
out-of-equilibrium dynamics before hydrodynamics is expected to be
valid. We describe how such behavior might be observed in real time in
ultracold atomic Fermi gases. We present an efficient way to compute
Green functions in real frequency beyond the derivative expansion and
discuss how the system relaxes toward equilibrium. On relevant time
scales, the dynamics is well represented by an analytical attractor
solution that is valid at shorter times before the onset of Navier-Stokes
hydrodynamics. The attractor represents an asymptotic series
at long times and is complemented by nonhydrodynamic modes.

Speaker: Tilman Enss

ERG2024_Enss.pdf

10:20 → 11:00 Central limit theorems, large deviations and the renormalization group

The Ising model at criticality is a paradigmatic example of random variables displaying strong correlations at all scales. While in the high and low temperature phases the collective properties of the system are described by the standard (Gaussian) central limit theorem, the critical point separating the two phases is captured by a scale invariant and universal asymptotic probability distribution. From a physicist point of view, the emergence of such probability distribution is understood using the renormalization group, which effectively describes the behavior of coarse-grained random variables.
In this talk, I will give a pedagogical overview of these concepts, using the probability distribution of the order parameter as an example of a non-trivial observable that can be computed using a functional version of the renormalization group. I will show that large deviations are universal, while very large deviation are non-universal. Furthermore, I will discuss how corrections-to-scaling can be rephrased in the langage of large deviations as a generalized Cramer's series.

Speaker: Adam Rançon

ERG_2024-Rancon.pdf

ERG_2024-Rancon.pptx

11:00 → 11:30 Break

11:30 → 12:10 Indications for particle physics from asymptotic safety

There is growing theoretical evidence for the existence of an interactive UV fixed point in the renormalization group flow of the dimensionless couplings of the gravitational effective action. In the Standard Model and/or in models of New Physics embedded in the framework of trans-Planckian asymptotic safety, the presence of such a fixed point imposes Planck-scale boundary conditions on the gauge, Yukawa and scalar couplings. The ensuing fixed-point analysis often allows one to derive specific predictions for the IR phenomenology. Interestingly, it can also lead to the dynamical generation of arbitrarily small quantities, like for example the Yukawa couplings of Dirac neutrinos. In my talk I will review a set of phenomenological predictions obtained in recent years in the framework of trans-Planckian asymptotic safety and discuss possible experimental signatures of such scenarios.

Speaker: Kamila Kowalska (National Centre for Nuclear Research)

2024.09.22_LesDiablerets_v2.pdf

12:10 → 12:50 Lorentzian Wetterich equations from the perturbative algebraic QFT perspective

In this talk I will present recent results obtained in collaboration with d’Angelo, Drago and Pinamonti. We proposed a new formulation of renormalisation group flow equations that work on arbitrary globally hyperbolic spacetimes and for any chosen Hadamard state. The examples treated so far include the scalar field, Yang-Mills theories and gravity.

Speaker: Kasia Rejzner

12:50 → 14:30 Lunch

14:30 → 15:50 Parallel A

14:30 Information geometry and the renormalization group

The talk reviews how a geometric approach to information theory and the functional renormalization group are closely connected. Information geometry defines distances on spaces of probability distributions, as well as further differential geometric structure like connections or curvature. In the context of field theories one can define on that basis geometrical structure on the space of theories which might help to better understand renormalization group flows.

Speaker: Stefan Floerchinger (University of Jena)

FloerchingerERG2024.pdf

14:50 Interacting UV fixed points and conformal windows of 4d super-Yang-Mills theories with matter

Using RG methods, I discuss perturbative and non-perturbative fixed points and conformal windows in 4d supersymmetric gauge theories coupled to matter and a superpotential. At weak coupling, I give an overview of perturbative UV and IR fixed points and their corresponding phase diagrams. At strong coupling, I discuss how conformal fixed points and superfield anomalous dimensions are identified using the method of a-maximisation and the infinite-order Novikov-Shifman-Vainshtein-Zakharov beta functions. Results are illustrated for SU(N) x SU(M) supersymmetric gauge theories, and implications for model building beyond the minimally supersymmetric Standard Model are indicated.

Speaker: Gabriel Picanco Costa

main.pdf

15:10 Influence of additional dimension-4 scalar operators on asymptotic safety in the Litim-Sannino model

We consider a four-dimensional $SU(N_c)$ gauge theory coupled to $N_f$ species of color fermions and $N_f^2$ colorless scalars. Compared to previous studies, we have included all possible trilinar and quartic scalar operators. In the regime where asymptotic freedom is absent, we determine all interacting fixed points using perturbation theory up to three loop in the gauge and two loop in the Yukawa and scalar couplings. We compared these results with those obtained previously \cite{Bednyakov:2023asy} without adding additional scalar operators. Moreover classical and quantum stability of the vacuum is discussed as well as the spectrum of anomalous dimensions of various operators.

Speaker: Alfiia Mukhaeva

15:30 A Probabilistic View of Renormalization Group Flows

I present a probabilistic framework to analyse global Renormalization Group Flows in large theory spaces. The framework allows to efficiently find basins of attraction, including fixed points of the linearized flow, as well as novel nonlinear attractors. As a working example, I discuss the gauge, Yukawa, and Higgs sector of the Standard Model of particle physics. I will also comment on naturalness and discuss how the framework can facilitate indirect Bayesian searches for new physics at energy scales which are inaccessible to direct observation.

Speaker: Aaron Held (Jena University)

14:30 → 15:50 Parallel B

14:30 Critical geometry approach to phase transitions

We devise a geometric description of bounded systems at criticality in dimension d (including d=3) [1]. This is achieved by altering the flat metric with a space dependent scale factor γ(x), x belonging to a general bounded , compact, domain Ω. γ(x) is chosen in order to have a scalar curvature to be constant and negative, the proper notion of curvature being -- as called in the mathematics literature -- the fractional Q-curvature. The equation for γ(x) is proposed to be the Fractional Yamabe Equation (to be solved in Ω) that, in absence of anomalous dimension, reduces to the usual Yamabe Equation in the same domain. From the scale factor γ(x) we obtain novel predictions for the scaling form of one-point correlation functions. We refer to this approach as the critical geometry approach. A (necessary) virtue of the proposed approach is that it encodes and allows to naturally retrieve the purely geometric content of two-dimensional boundary conformal field theory. From the critical magnetization profile in presence of boundaries one can extract the scaling dimension of the order parameter, Δϕ. For the 3D Ising model [1] we find Δϕ=0.518142(8) which favorably compares (at the fifth decimal place) with the state-of-the-art estimate. A nontrivial prediction is the structure of two-point correlators at criticality. They should depend on the fractional Q-hyperbolic distance calculated from the metric, in turn depending only on the shape of the bounded domain and on Δϕ. Results obtained using the critical geometry approach for the 4D Ising model, the 3D XY model and the 3D percolation are also presented. Finally, comments on the long-range interacting case will be presented. [1] G. Gori and A. Trombettoni, "Geometry of bounded critical phenomena", J. Stat. Mech. 063210 (2020).

Speaker: Andrea Trombettoni

14:50 Conformal constraints and the derivative expansion

In the last two decades, the derivative expansion has been employed with great success to compute physical quantities in critical phenomena within the non-perturbative renormalization group. This success was achieved by implementing the approximation scheme to high orders which brought, alongside, various conceptual insights regarding its behaviour. The general idea relies on finding fixed points of the non-perturbative renormalization group flow equation, which is equivalent to the Ward-identity for dilatations, by considering a certain ansatz expression for the effective action with all possible terms up to a given number of derivatives. Additionally, at these fixed points conformal symmetry is expected to take place as an emergent property of the system instead of only exhibiting scale invariance. This opens the door for the use of information or constraints arising from conformal symmetry in order to compute physical quantities in this physical regime. In this talk we discuss conformal symmetry constraints for the vertices at the fixed point and how is the behaviour of these constraints within the derivative expansion applied to the Ising model universality class. This allows for the use of conformal invariance as a way of fixing spurious parameters within the derivative expansion. We then propose a way to rethink this conformal constraints and propose a new way of implementing the derivative expansion when conformal symmetry is realized and show results regarding the quality and precision of this approximation scheme.

Speaker: Gonzalo De Polsi

15:10 Instantons within the Functional renormalization group

As spatial dimensionality gets lower it becomes more difficult for a system to order. At some dimensionality, the so called lower critical dimension, the fluctuations prevent ordering all together and the only way to order is to put temperature to 0. We discuss the scenario of the approach to lower critical dimension within the Functional renormalization group (FRG) for the scalar $\varphi^4$ theory. There we expect localized, instanton-like (kink-like) excitations to proliferate and the fixed point to disappear. Despite FRG seemingly being a correct tool for the job, capturing this scenario has proven to be a difficult problem and one typically obtains the possibility of ordering where it should not be possible [1,2]. We uncover the analytical structure of the FRG that allows us to understand the source of the problem [3]. Remarkably we indeed find that FRG captures the localized instantonic excitations, albeit in a rather indirect way. We shall discuss the applications of our work to some open problems that we believe we can elucidate, for example: a) quantum mechanical tunneling problem in the low temperature limit which appears in description of the Sine-Gordon problem [4]; b) the question of lower critical dimension in hysteresis [5]. References [1] Ken-Ichi Aoki, Atsushi Horikoshi, Masaki Taniguchi and Haruhiko Terao: “Non-Perturbative Renormalization Group Analysis in Quantum Mechanics”, Progress of Theoretical Physics 108 571 (2002) [2] Alfio Bonanno,Alessandro Codello and Dario Zappalà: “Structural aspects of FRG in quantum tunneling computations”, Annals of Physics 445 169090 (2022), [3] Lucija Nora Farkaš, Gilles Tarjus, Ivan Balog: “Approach to the lower critical dimension of the $\varphi^4$ theory in the derivative expansion of the functional renormalization group”, Physical Review E 108 054107 (2023) [4] Romain Daviet and Nicolas Dupuis: “Nature of the Schmid transition in a resistively shunted Josephson junction”, Phys. Rev. B 108, 184514 (2023) [5] D. Spasojević, S. Janićević, and M. Knežević,: “Numerical Evidence for Critical Behavior of the Two-Dimensional Nonequilibrium Zero-Temperature Random Field Ising Model” Physical Review Letters 106, 175701 (2011)

Speaker: Ivan Balog

IB_instantons_and_dl_ERG2024.pdf

15:30 Probability distribution function of the 2d Ising order parameter

The question of the probability distribution of the sum of random variables has suscited considerable attention from various fields of physics and mathematics. While the case of uncorrelated variables is described by the central limit theorem and its extensions, that of strongly correlated variables is more complicated. Turning our attention to the canonical example of strongly correlated variables, Ising spins close to criticality, we discuss the rate function that describes the statistics of their sum, the field theoretical formalism that allows us to compute it and present results obtained from the nonpertrubative functional renormalization group. In particular, while in 3d a simple local potential approximation is enough to reproduce the rate function, in 2d, owing to the stronger correlations at the fixed point, it is necessary to go beyond. We show that taking into account the momentum dependence of the correlation functions is crucial to correctly reproduce the rate function, which we account for by means of the celebrated Blaizot-Mendez--Galain-Wschebor approximation.

Speaker: Félix Rose

Rose_PDF_FRG.pdf

15:50 → 16:20 Break

16:20 → 18:00 Parallel A

16:20 Wilsonian RG for 3D Wess-Zumino--Witten theory with Stiefel-manifold target space

A Stiefel manifold for $N, p$ integers with $N > p$ is the quotient $\operatorname{SO}(N)/\operatorname{SO}(p)$. In $d = p - 1$ spacetime dimensions (set henceforth $d = 3$), it admits a non-trivial Wess-Zumino--Witten theory. Here, I shall present efforts to study which of these theories admit real fixed points of the renormalisation group flow. I shall work in a Wilsonian implementation, using a weak-coupling expansion for general $N$ and a self-consistent scheme for $N=5$ (the latter based on work with Hawashin-Eichhorn-Janssen-Scherer). It is well known that these theories describe (quasi-)universal properties of exotic phase transitions and phases beyond the Ginzburg--Landau paradigm, with explicit microscopic realisations known at least for $N = 5,6$. For $N > 6$, no known (super-)renormalisable dual Lagrangian is known, rendering them of great intrinsic theoretical interest as well.

Speaker: Shouryya Ray

16:50 Physics-informed renormalisation group flows

The physics of strongly correlated systems offers some of the most intriguing physics challenges such as competing orders or the emergences of dynamical composite degrees of freedom. Often, the resolution of these physics challenges is computationally hard, but can be enormously simplified by its formulation in the dynamical degrees of freedom and within an expansion about the physical ground state. Importantly, such a formulation does not only reduce or minimise the computational challenges, it also facilitates the access to the physics mechanisms at play. The tasks of finding the dynamical degrees of freedom and the physical ground state can be systematically addressed within the functional renormalisation group approach with flowing fields which accommodates both, emergent composites as well as the physical ground state.

In the present talk I will discuss how to use this approach for setting up \textit{physics-informed flows} (PI flows): Scale-dependent coordinate transformations in field space induce flowing fields, and the respective flows for the effective action generate a large set of pairs of \textit{target actions}, formulated in emergent composite fields. The potential uses of PI flows are manifold: to begin with, they allow for a systematic search of the dynamical degrees of freedom and the respective ground state that leads to the most rapid convergence of expansions schemes thus minimising the computational effort (lower simplicity bound). Secondly, the resolution of the remaining computational tasks within a given expansion scheme can be further reduced by optimising the physics content within a given approximation. Thirdly, the maximal variability of PI flows can be used for reducing the analytic and numerical effort of solving the flows within a given approximation.

Speaker: Friederike Ihssen (ITP Heidelberg)

ERG2024_upload.pdf

17:20 Towards the phase diagram of QCD and its critical endpoint

I report on technical advancements which are geared towards locating the conjectured critical endpoint of QCD using the functional renormalization group. Its use allows to access directly the high-density region, as this approach does not suffer from the sign problem of lattice QCD. In our first-principles setup, one can systematically identify and include all relevant physical degrees of freedom, which is a current work in progress. I discuss both quantitative results in the vacuum as well as the extension to the phase diagram up to intermediate densities, including arbitrary-order meson interactions and full momentum dependences. Furthermore, I discuss an analysis of the systematic error of such an fRG calculation of QCD. Finally, for calculations at even higher densities, I discuss future extensions of our setup, such as other potentially relevant composite particles.

Speaker: Franz Richard Sattler

2024_09_Sattler_QCD.pdf

17:40 Quantum field theories of relativistic Luttinger fermions

We propose relativistic Luttinger fermions as a new ingredient for the construction of fundamental quantum field theories. We construct the corresponding Clifford algebra and the spin metric for relativistic invariance of the action using the spin-base invariant formalism. The corresponding minimal spinor has 32 complex components, matching with the degrees of freedom of a standard-model generation including a right-handed neutrino. The resulting fermion fields exhibit a canonical scaling different from Dirac fermions and thus support the construction of novel relativistic and perturbatively renormalizable, interacting quantum field theories. In particular, new asymptotically free self-interacting field theories can be constructed, representing first examples of high-energy complete quantum field theories based on pure matter degrees of freedom. We then investigate a class of quantum field theories with self-interacting relativistic Luttinger fermions using mean-field theory to explore their long-range behaviour with a classification of the set of possible mass terms that can be constructed.

Speaker: Marta Picciau

Picciau_ERG2024.pdf

16:20 → 18:00 Parallel B

16:20 Multiscale Functional Renormalization Group Approach to the 1D Extended Hubbard Model

We review our recent development of the Multiscale Functional Renormalization Group (MFRG) as an approach to the study of strongly correlated electronic materials in which both electron-electron (e-e) and electron-phonon (e-ph) interactions play important roles. Our MFRG method includes in a systematic manner the effects of the scattering processes involving electrons away from the Fermi surface and also permits proper inclusion of phonon retardation effects. After introducing the basic concepts, I will discuss in detail the application of this method to the 1D Extended Hubbard model and show that it correctly captures the subtle bond-order wave (BOW) phase in that model.
We will then discuss additional applications of the MFRG method and show that it can be applied to multi-band models in higher dimensions, recovering previously known results and predicting novel behaviors that have been seen in experiment. Finally, we will discuss possible future applications of the MFRG approach.

Speaker: David K. Campbell

16:50 Quantum critical Dirac semimetals and finite-temperature effects

The chiral Ising-, XY-, and Heisenberg models serve as effective descriptions of Dirac
semimetals undergoing a quantum phase transition into a symmetry-broken ordered
state. Interestingly, their quantum critical points govern the physical behavior of the system in the vicinity of the transition even at finite temperatures. In this contribution,
we explore the chiral models at zero and finite temperature, both in the Dirac phase
as well as in the symmetry-broken phases. To that end, we set up a functional
renormalization group approach, which allows us to systematically track (1) the
phenomenon of pre-condensation, (2) the manifestation of the Mermin-Wagner-
Hohenberg theorem due to pseudo-Goldstone fluctuations at finite temperatures, and
(3) the quantitative behavior of the system in the quantum critical fan, e.g., by
calculating the quasiparticle weight. Our work aims at a more holistic understanding
of chiral models near their quantum critical point, including, e.g., the description of non-Dirac-liquid behavior, in analogy to the non-Fermi-liquid behavior in metallic
quantum critical points.

Speaker: Mireia Tolosa Simeon

17:20 New universality class describes Vicsek's flocking phase in physical dimensions

The Vicsek simulation model of flocking together with its theoretical treatment by Toner and Tu in 1995 were two foundational cornerstones of active matter physics. However, despite the field's tremendous progress, the actual universality class (UC) governing the scaling behavior of Viscek's "flocking" phase remains elusive. Here, we use nonperturbative, functional renormalization group methods to analyze, numerically and analytically, a simplified version of the Toner-Tu model, and uncover a novel UC with scaling exponents that agree remarkably well with the values obtained in a recent simulation study by Mahault et al. [Phys. Rev. Lett. 123, 218001 (2019)], in both two and three spatial dimensions. We therefore believe that there is strong evidence that the UC uncovered here describes Vicsek's flocking phase.

Speaker: Patrick Jentsch

ERG24 - PJentsch.pdf

17:40 Optimization and Stabilization of Functional Renormalization Group Flows

We revisit optimization of functional renormalization group flows by analyzing regularized loop integrals. This leads us to a principle, the Principle of Strongest Singularity, and a corresponding order relation which allows to order existing regularization schemes with respect to the stability of renormalization group flows. Moreover, the order relation can be used to construct new regulators in a systematic fashion. For studies of critical behavior, which require to follow renormalization group flows down to the deep infrared regime, such new regulators may turn out to be particularly useful. The general application of this principle is demonstrated with the aid of a scalar field theory which is solved over a wide range of scales with novel methods borrowed from numerical fluid dynamics.

Speaker: Niklas Zorbach

18:00 → 19:00 Welcome reception

Welcome
Tribute to Ulrich Ellwanger by Jan Pawlowski
Aperitif

19:00 → 20:00 Dinner

Tuesday 24 September

09:00 → 09:40 Finite formulation of QFT, naturalness, and the effective action

I will provide an overview of the finite formulation of Quantum Field Theory (QFT) using the Callan-Symanzik method. This method enables the calculation of correlation functions without encountering intermediate divergences. I will discuss the impact of this technique on the hierarchy problem and naturalness, as well as its application to the quantum effective action in both renormalizable and non-renormalizable theories.

Speaker: Mikhail Shaposhnikov (EPFL - Ecole Polytechnique Federale Lausanne (CH))

Finite_Diablerets_shown.pdf

09:40 → 10:20 Renormalization of Effective Field Theories from Geometry

The renormalization group equations (RGE) are a necessary component to comparing physics at different scales. For renormalized quantum field theories (QFT), there exists algebraic formulae, derived by ’t Hooft, which encode the one-loop counterterms of a wide class of theories. After reviewing how they were derived, we will extend to two-loop counterterms for scalar QFT. Moreover, we will see how these formulae can be applied to effective field theories (EFT) — theories with non-renormalizable higher-order operators — thanks to the geometric picture of EFT.

Speaker: Julie Pagès

EFT_Geometry_JPages.pdf

10:20 → 11:00 Asymptotic Safety and Vacuum Stability in the Litim-Sannino Model

I will review the progress in the Litim-Sannino model, where Asymptotic Safety occurs in a perturbatively controlled manner. Recent computations of three- and four-loop RGEs has opened new pathways to estimate the width of the UV conformal window. I will discuss the methods and phenomena constraining the window. In this regard, the stability of the scalar potential is an important observable. I will present how high-quality predictions are obtained from the quantum-improved potential.

Speaker: Tom Steudtner

steudtner.pdf

11:00 → 11:30 Break

11:30 → 12:10 Trace anomaly and renormalization group

I will review several aspects of the trace anomaly and its relation with the renormalization group.

Speaker: Omar Zanusso

erg2024_Zanusso.pdf

12:10 → 12:50 Nonperturbative QCD within the functional renormalization group

In this talk, I would like to discuss recent progress in studies of nonperturbative QCD within the functional renormalization group (fRG) approach, focusing mainly on three aspects: QCD in vacuum and hadron structure, QCD at finite temperature and densities, and real-time dynamics of QCD. This concerns in more detail on the construction of fRG approach to first-principles QCD within the four-quark scatterings, and its application to the calculation of quasi-parton distribution amplitudes (PDA) for pions, QCD phase diagram and location of the critical end point (CEP), ripples of CEP, soft modes and the size of the static and dynamic critical region, the QCD moat regime, relaxation dynamics in QCD, etc.

Speaker: Wei-jie Fu (Dalian University of Technology)

Fu-ERG2024.pdf

12:50 → 14:30 Lunch

14:30 → 16:10 Poster Session

14:30 A new universality class describes Vicsek's flocking phase in physical dimensions

The Vicsek simulation model of flocking together with its theoretical treatment by Toner and Tu in 1995 were two foundational cornerstones of active matter physics. However, despite the field's tremendous progress, the actual universality class (UC) governing the scaling behavior of Viscek's "flocking" phase remains elusive. Here, we use nonperturbative, functional renormalization group methods to analyze, numerically and analytically, a simplified version of the Toner-Tu model, and uncover a novel UC with scaling exponents that agree remarkably well with the values obtained in a recent simulation study by Mahault et al. [Phys. Rev. Lett. 123, 218001 (2019)], in both two and three spatial dimensions. We therefore believe that there is strong evidence that the UC uncovered here describes Vicsek's flocking phase.

Speaker: Patrick Jentsch

14:30 An analysis of the regularization scheme dependence in low-energy effective field theories

Low-energy models are often used to study properties of strong-interaction matter, in particular at low temperatures. We investigate regularization scheme dependences of the quark-meson model in the mean-field and local potential approximation. To this end, we work out a meaningful comparison procedure for calculations with different regularization schemes using renormalization-group consistency. In the mean-field approximation, comparability can trivially be achieved and we find no regularization scheme dependence at all. In the local potential approximation comparability is non-trivial, but where a comparison is possible, regularization scheme artefacts are found to be small.

Speaker: Jonas Stoll

14:30 Asymptotically safe gauge-gravity systems

Asymptotically safe quantum gravity might cure the Landau pole of the Abelian hypercharge-sector of the Standard Model by adding a screening contribution to its scale-dependence, ultimately rendering it asymptotically free. On the other hand, gravitational fluctuations also induce higher order gauge-field operators, which cannot be set to zero consistently at high energies. These can lead to constraints on the gravitational parameter space from consistency conditions in the UV and in the IR. In this talk, I will review key aspect of the gauge-gravity system, and assess their robustness under changes of the gauge, and regulator, and upon extensions of the truncation.

Speaker: Marc Schiffer

14:30 Building nuclear Energy Density Functionals with the FRG

Since two decades, Ab Initio methods in nuclear physics have have undergone considerable development. These methods have two pillars : on one hand interactions between nucleons are derived order by order from chiral EFT ; on the other hand many-body techniques are applied to solve the Schrödinger equation. Such methods have provd successful and reliable in describing the properties of nuclei up to mass A ~ 100. Due to their prohibitive numerical scaling, these many—body methods are bound to fail in heavier systems. It is therefore necessary to develop another efficient framework for dealing with heavier masses. It has been shown that such systems can be understood at a mean-field-like cost within the framework of Energy Density Functional (EDF) framework . At present, the interactions involved, are purely empirical and therefore lack a proper theoretical foundation. In the present work, we aim to derive such "in-medium" interactions from a "bare" interaction describing nucleon-nucleon scattering using FRG methods.

Speaker: Louis Heitz

14:30 Critical dynamics with the aFRG

Euclidean approaches such as the functional renormalization group (FRG) have been abundantly and successfully used to study the universal static critical behavior of various physical systems near continuous phase transitions. For the study of critical dynamics, on the other hand, one usually relies on real-time methods. Our research aims to connect and relate the two approaches by comparing analytically continued (aRG) and real-time FRG on the closed time path. In particular, we investigate the dynamic critical behavior of a dissipative open quantum system near equilibrium in the spirit of the Caldeira-Leggett model with the aFRG and compare that with real-time results for the dynamic universality class of the corresponding Model A (according to the classification by Halperin and Hohenberg). The long-term goal of this project is to understand the merits and limitations of studying more complicated critical dynamics, including conservation laws and reversible mode couplings as relevant for QCD, with analytically continued Euclidean versus real-time approaches.

Speaker: Patrick Niekamp

14:30 Diagrammatic analysis of Anderson's orthogonality catastrophe

The study of the Fermi-edge singularity in x-ray absorption spectra of metals is a paradigmatic fermionic model, which exhibits logarithmic divergences in perturbation theory. Thus, it offers a playground for different diagrammatic approximations. It has been shown that a summation of parquet diagrams and, even more restricted, a 1-loop fRG approach are sufficient to include all leading-logarithmic terms of the model. Our motivation is to investigate the model beyond that and give a diagrammatic description of Anderson's related orthogonality catastrophe. For this, we developed a parquet solver using Matsubara formalism, which includes all components of the four-point vertex in a theory with two particle types. The recently introduced single-boson exchange (SBE) decomposes the four-point vertex into diagrams with lower frequency dependences simulating effective bosonic interactions. We make use of the SBE decomposition and show that multi-boson exchange (MBE) diagrams need to be taken into account in order to correctly include all the leading-logarithmic contributions of the model.

Speaker: Marcel Gievers

14:30 Dilaton Quantum Gravity

In this talk, I will present the Dilaton Quantum Gravity in the context of the Asymptotic Safety Scenario. We consider a scalar field non-minimally coupled to gravity a la Brans-Dicke and after deriving the corresponfing flow equations for the couplings (now functions of the scalar field), we first explore the behavior of the system on its fixed point. Performing a large field expansion in terms of the scalar field we find a constant dependence on it and use the latter as input for the computation of the full dependence of the functions on the scalar field, still on the fixed point. We then flow away from the UV using different perturbations around the fixed point as our intitial conditions and derive the infrared functions of the theory.

Speaker: Athanasios Kogios

14:30 Exploring the landscape of large-N fermionic theories

Theories of self-interacting fermions play an important role in particle and condensed matter physics, covering effective descriptions of the strong nuclear force, the critical behaviour of Dirac materials such as graphene, and more. In this talk, I discuss functional RG flows for fermionic systems in the large-N limit. Working directly in terms of fermionic field variables and using a Fierz-complete basis of bilinears, I provide conditions under which fermionic flows become exact, and exactly solvable, and provide the most general form of their quantum effective actions. I exemplify the method for fermionic theories with scalar, pseudo-scalar, vector, axial-vector, and derivative interactions in various dimensions. Results include phenomena such as chiral symmetry breaking and dynamical generation of fermion mass, interacting fixed points, universal scaling dimensions of operators, conformal manifolds with exactly marginal interactions, the spontaneous breaking of scale symmetry, and the appearance of a massless dilaton. Exact dualities with bosonised versions of theories are also discussed.

Speaker: Charlie Cresswell-Hogg

14:30 Fermionic self energy near quantum criticality in two dimensions

We study the functional renormalization group flows of fermionic self energy close to quantum criticality in two dimensional systems of fermions coupled to a collective order parameter mode. Taking into account the flow of the bosonic mass we analyze how the non-Fermi liquid state is generated upon reducing the cut-off scale close to the quantum criticality. Within our framework we capture the crossover to the standar Fermi liquid behaviour while detuning the system from the quantum critical point at temperature T=0 and T>0.

Speaker: Mateusz Homenda

14:30 fRG Analysis and Fluctuation Diagnostics of the Hubbard-Holstein Model

Recently, due to tremendous progress in materials synthesis the family of strongly-correlated systems exhibiting superconductivity has been extended substantially, e.g., through the experimental study of magic-angle bilayer graphene and other graphene-based heterostructures, and more. Yet, the origin of the superconducting pairing mechanism(s) in these materials is far from being clear as both, Coulomb interactions and electron-phonon couplings can become sizable. This brings a long-standing question back to our attention, namely, what is the interplay between electron-electron and electron-phonon interactions in strongly-correlated electron systems on a lattice. The functional renormalization group is a prime tool to approach this problem as it allows us to treat all interaction channels on equal footing. To explore the interplay of Coulomb and electron-phonon interactions, however, retaining frequency dependencies of the vertices and the self-energy is required, which requires the development of efficient algorithms. Here, we report on the development of a physically transparent, accurate, and efficient fRG scheme based on single boson exchanges. As a paradigmatic study, we explore the Hubbard-Holstein model on the square lattice. Concretely, we can quantitatively compare to recent numerical studies at half filling, but also extend our analysis to regions away from half filling, which are inaccessible to quantum Monte-Carlo simulations. In the spirit of “fluctuation diagnostics”, we explore directly the influence of phonons on the electronic susceptibilities at half-filling and at finite doping. By reconstructing the phonon-self energy, we also investigate the effect of electrons on the phonons and the lattice.

Speaker: Aiman Al-Eryani

14:30 Functional renormalization group for the Hubbard model at infinite on-site repulsion via Hubbard X-operators

Exact functional renormalization group (FRG) flow equations for quantum systems can be derived directly within an operator formalism without using functional integrals. This simple insight opens new possibilities for applying FRG methods to models for strongly correlated electrons with projected Hilbert spaces, such as the t model, obtained from the Hubbard model at infinite on-site repulsion. By representing this model in terms of Hubbard X-operators, we derive exact flow equations for the time-ordered correlation functions of the X-operators (X-FRG), which allow us to calculate the electronic correlation functions in the projected Hilbert space. We use our approach to investigate the ``hidden Fermi liquid'' state of this model where the Hamiltonian consists only of the projected kinetic energy.

Speaker: Jonas Arnold

14:30 Generalization of the Central Limit Theorem to critical systems: A Perturbative Approach

The Central Limit Theorem does not hold for strongly correlated stochastic variables, as is the case for statistical systems close to criticality. Recently, the calculation of the probability distribution function (PDF) of the magnetization mode has been performed with the functional renormalization group (FRG) in the case of the three dimensional Ising model . We show how this PDF or, equivalently, the rate function which is its logarithm, can be systematically computed perturbatively in the $\epsilon=4-d$ expansion. At the price of making an RG improvement functionally, we find that our results compare very well with the FRG calculations and Monte Carlo simulations even for the tail of the distribution, that is, at large magnetization. This holds true for the entire family of universal PDFs parameterized by $\zeta=\lim_{L,\xi_\infty\rightarrow\infty} L/\xi_\infty$ which is the ratio of the system size $L$ to the correlation length $\xi_{\infty}$ with both the thermodynamic limit and the critical limit being taken simultaneously.

Speaker: Sankarshan SAHU

14:30 Higher spin theory/O(N) vector model duality and Exact Renormalisation Group

It has been conjectured that the 3d free O(N) vector model has an AdS4 dual which is Vasiliev's higher spin theory. Higher spins naturally arise in string theory, and they could soften the UV properties of quantum gravity. Since the boundary theory is a free theory, this duality is an ideal setting to understand higher spin theory through the much simpler free O(N) model. In fact, Vasiliev's theory is described in terms of equations of motion with a large number of auxiliary fields, and no action is known. In this context, there have been attempts to build the higher spin theory holographically from the free O(N) model. We will describe how Polchinski's ERG of the boundary currents can give us the bulk partition function with the action for the massless higher spin fields upto cubic order.

Speaker: Pavan Dharanipragada

14:30 Hydrodynamic Transport: From QFT to a Shear Viscosity Coefficient using the FRG

Hydrodynamics is an effective, long-range field theory whose properties emerge from the underlying short-range behaviour. The description of dissipative fluids needs knowledge about transport coefficients like viscosities or conductivities that govern the relaxation of a system back to its equilibrium state and depend solely on the systems microscopic properties. In this talk I will present an approach to calculate a shear viscosity coefficient emergent from a real, massive, interacting scalar quantum field theory using the Wetterich equation at finite temperature, introduced via the imaginary time formalism. A flow equation of the viscosity coefficient is given in the framework of linear response theory and solved to extract the temperature dependence even beyond the perturbative regime. Furthermore a truncation is developed which incorporates dissipative effects like 'Landau damping' by introducing discontinuous terms that capture the appearance of a thermal decay width due to heat-bath interactions.

Speaker: Tim Stötzel

14:30 Information-theoretical aspects of renormalization group

We demonstrate that quantum error correction is realized by the renormalization group in scalar field theories. We construct q-level states by using coherent states in the IR region. By acting on them the inverse of the unitary operator U that describes the renormalization group flow of the ground state, we encode them into states in the UV region. We find that the Knill-Laflamme condition is satisfied for operators that create coherent states. We verify this to the first order in the perturbation theory. This result suggests a general relationship between the renormalization group and quantum error correction and should give insights into understanding a role played by them in the gauge/gravity correspondence. Based on the result, we discuss some prospects for the renormalization group and its information theoretical aspects.

Speaker: Ryota Nasu

14:30 Interplay of chiral transitions in the standard model

We investigate nonperturbative aspects of the interplay of chiral transitions in the standard model in the course of the renormalization flow. We focus on the chiral symmetry breaking mechanisms provided by the QCD and the electroweak sectors, the latter of which we model by a Higgs-top-bottom Yukawa theory. The interplay becomes quantitatively accessible by accounting for the fluctuation-induced mixing of the electroweak Higgs field with the mesonic composite fields of QCD. In fact, our approach uses dynamical bosonization and treats these scalar fields on the same footing. In the first project we look at the changed infrared behaviour of the theory under inclusion of the QCD sector, compared to the pure Higgs-top-bottom model, with a focus on studying the naturalness problem in the model. In the current project we investigate UV completions within the Higgs-QCD model, a first analysis shows the existence of CEL-like scaling solutions.

Speaker: Richard Schmieden

14:30 Lorentzian functional renormalization and the Nash-Moser theorem

The Renormalization Group (RG) Equation determines the flow of the effective action under changes in an artificial energy scale, which roughly corresponds to the scale of the system under consideration. I report on a rigorous construction of a non-perturbative RG flow for the effective action in Lorentzian manifolds. I give the main ideas of a proof of local existence of solutions for the RG equation, when a suitable Local Potential Approximation is considered. The proof is based on an application of the renown Nash-Moser theorem. Time permitting, I also discuss an application of the RG equation to the non-perturbative renormalizability of quantum gravity.

Speaker: Edoardo D'Angelo

14:30 On harvesting physical predictions from asymptotically safe quantum field theories

Asymptotic safety is a powerful mechanism for obtaining a consistent and predictive quantum field theory beyond the realm of perturbation theory. It hinges on an interacting fixed point of the Wilsonian renormalization group flow, which controls the microscopic dynamics. Connecting the fixed point to observations requires constructing the set of effective actions compatible with this microscopic dynamics. Technically, this information is stored in the UV-critical surface of the fixed point. In this talk, I will describe a novel approach for extracting this information based on analytical and pseudo-spectral methods. I will illustrate the methods at the level of the two-dimensional Ising model, where we find non-trivial predictions for the effective action. The developed techniques apply to any asymptotically safe quantum field theory. Furthermore, they also constitute an important step towards setting up a well-founded swampland program within the gravitational asymptotic safety program. The talk is based on arXiv:2403.08541.

Speaker: Agustín Silva

14:30 Phase Structure of the Quark-Meson-Diquark Model

We study a quark-meson-diquark model with omega vector meson, including the fluctuations of the sigma and pion, in an LPA truncation. We discuss the effect of the sigma and pion fluctuations on the phase structure and the equation of state. The effects of different diquark and vector couplings are also investigated.

Speaker: Ugo Mire

14:30 Physical running in quadratic gravity

Running coupling were introduced in quantum filed theory in order to preserve perturbativity in scattering amplitudes, despite the appearance of large logs of external momenta. It is commonly believed that these logarithms are directly related to UV divergencies in one-loop perturbation theory, however this is not completely true in higher derivative theories, where large logs can emerge also from UV finite loop integrals due to IR effects and, on the other hand, some UV divergent diagrams do not depend on external momenta. We define a new set of beta functions for quadratic gravity based on the explicit computation of large logs of momenta and discuss their features concerning the asymptotic UV behavior of the theory. In particular, we observe the existence of a unique trajectory of the perturbative RG leading to asymptotic freedom without presence of tachyons.

Speaker: Diego Buccio

14:30 Quark-Meson model from the real-time functional renormalization group

In this work, Quark-Meson model is formulated in real-time, taking into account the dynamic properties (dissipation of $\sigma$ and $\pi$) by considering the system interacting with a heat bath. The symmetry of thermal equilibrium of the real-time action combined fermionic system is studied. Real-time functional renormalization group method is employed to study the flow of the effective potential and it is found that the dynamic properties of the system does have influence on the static observables but the influence is minor. We compare the phase diagrams and static observables such as screening masses and condensates under zero damping, physical damping and infinite damping.

Speaker: Yunxin Ye

14:30 Realtime quantities from spectral flows and other functional methods

In this talk, we report on recent results within spectral functional methods. We focus in particular on spectral Callan-Symanzik flows and the computation of spectral functions in the scaling limit of a scalar theory, the Quark-Meson model and gravity. Furthermore, discuss spectral Bethe-Salpeter equations at the example of a scalar theory and the extension of the spectral funtional framework to finite temperature at the example of the Quark spectral function, which allows direct computation of transport coefficient.

Speaker: Jonas Wessely

14:30 Renormalization Flow of Nonlinear Electrodynamics

We study the renormalization flow of generic actions that depend on the invariants of the field strength tensor of an abelian gauge field. While the Maxwell action defines a Gaussian fixed point, we search for further non-Gaussian fixed points or rather fixed functions, i.e., globally existing Lagrangians of the invariants. For the construction of a globally existing fixed function, we pay attention to the use of proper initial conditions. Our results provide evidence for the existence of a continuum of non-Gaussian fixed points parametrized by a small positive anomalous dimension below a critical value. For the strong-field limit of the 1PI QED effective action, where the anomalous dimension is determined by electronic fluctuations, our result suggests the existence of a singularity free strong-field limit, circumventing the standard conclusions connected to the perturbative Landau pole.

Speaker: Julian Schirrmeister

14:30 Renormalized mean-field form of the static spin correlator and approximate nature of the quantum-to-classical correspondence

The quantum-to-classical correspondence (QCC) in spin systems is the phenomenon that the static correlator of quantum spin models agree with their classical counterpart at a different temperature within QMC error bars in bold-line diagrammatic Monte-Carlo. The quantum fluctuations appear to only "heat up" the system. Currently, the QCC is a purely empirical observation. We show that the QCC is exact until 3rd order perturbation theory in any dimension and for all spin lengths, and universally breaks down at fourth order. The QCC thus never holds exactly. We give a model dependent equation for the correspondence in 3rd order perturbation theory. Furthermore, we uncover why the QCC can be observed in the first place. We show that whenever QCC is observed, the static correlator of quantum and classical models can be approximated by a renormalized mean-field correlator. This is due to a partial cancellation of 1J-irreducible diagrams that contribute to deviations from the renormalized mean-field correlator. With this new insight, we are able to reproduce the spin structure factor for $\mathrm{K}_2\mathrm{Ni}_2(\mathrm{SO}_4)_3$ where a QCC was previously observed.

Speaker: Benedikt Schneider

14:30 Scalar and TT mode spectral functions of Lorentzian quantum gravity

We compute the asymptotically safe graviton propagators of the transverse-traceless and scalar mode within Lorentzian quantum gravity. To that end, we determine the interacting UV fixed point in Lorentzian signature, find connecting UV-IR trajectories, and solve the coupled system of running Kallen-Lehmann spectral representations. The resulting spectral functions are compatible with causality and unitarity. Furthermore, they provide direct access to the full quantum propagators, the corresponding Weyl-tensor and Ricci-scalar form factors in the quantum effective action, and UV scaling dimensions.

Speaker: Gabriel Assant

14:30 Scaling exponents in quantum gravity

I will discuss how scaling exponents in quantum gravity can be defined for diffeomorphism invariant operators. I will the report recent progress on the computation of the exponents using the essential renormalisation group.

Speaker: Kevin Falls

14:30 Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the fRG

We extend the recently introduced single-boson exchange (SBE) formulation to the computation of the self-energy from the Schwinger-Dyson equation. In particular, we derive its general expression both in diagrammatic and in physical channels and show that the SBE formulation of the Schwinger-Dyson equation can be naturally applied also to non-local interactions. We furthermore discuss its implications in a truncated unity solver. As an application, we provide fRG results for the two-dimensional Hubbard model at weak coupling, where the use of the Schwinger-Dyson equation for the self-energy flow allows to capture the pseudogap opening. We illustrate that the SBE formulation proves particularly advantageous in identifying the relevant physical channels that drive the physical behavior. The expressions obtained for the self-energy rely on a single-channel parametrization, allowing further investigations within a fluctuation diagnostic of the different self-energy contributions, and this would enable to establish a comprehensive framework applicable to models with a non-local interaction or an $SU(2)$ symmetry broken phase. We discuss the extension to the strong coupling regime by combining the fRG with dynamical mean-field theory (DMFT) in the so-called DMF2RG.

Speaker: Miriam Patricolo

14:30 TBA

Speaker: Yuepeng Guan

14:30 TBA

Speaker: Yadikaer Maitiniyazi

14:30 The NPRG derivative expansion of O(N) models: conformal symmetry constraints and the principle of minimum sensitivity

It is well known that the symmetries of a theory often restrict its form, and sometimes allow to totally determine it. In particular, it has been long conjectured that the O(N) models’ critical regime is characterized by the presence of the complete conformal symmetry. Moreover, it has been proven for the specific values of N=1, 2, 3 and 4, that this is in fact the case. There exist numerous physical systems falling into O(N) universality classes for different values of N: pure substances and uniaxial magnets for N=1, -transition of liquid Helium-4 and planar magnets for N=2 or isotropic magnets for N=3, to mention but a few. Within the derivative expansion of the non-perturbative renormalization group for the O(N) models, special-conformal symmetry provides extra constraints which make the theory overdetermined and are, thus, not exactly fulfilled once the approximation is performed. In this study we extend previous works on the Ising universality class in which the non-physical parameters of the approximation – those that characterize the regulating function – are fixed by minimizing the breaking of the special conformal restrictions coming from the Ward-Takahashi identities for the vertices. We refer to this criterion as the Principle of Maximum Conformality (PMC). In this work, we numerically study this breaking for both the relevant perturbation of the fixed point, identified with the critical exponent ν, as well as for the least irrelevant perturbation, connected with the first correction to the long-distance scaling – the critical exponent, ω. Our results show that special conformal symmetry does indeed seem to be fulfilled in the critical regime of O(N) models, including examples without a clear unitary realization (N=0 and N=-2). More interestingly, we obtain results equivalent, for all practical purposes, to those coming from the Principle of Minimum Sensitivity (PMS). Considering this, we conclude that the PMS does not only reduce the spurious dependence on non-physical parameters, but also minimizes the breaking of the symmetries of the theory. Although the convergence properties of the DE are still to be completely understood, it was recently observed the existence of a parameter of order ¼ which regulates the convergence between successive orders. Additionally, from numerical results, it appears that the PMS criterion provides the estimations which converge fastest. Following this line, our present work suggests that seeking the best satisfaction of the conformal symmetry does in turn make the method converge faster – as the PMC and PMS criteria seem to be equivalent for the studied O(N) model cases.

Speaker: Santiago Cabrera Sosa

14:30 Towards nonperturbative nonlocal correlations in the 2d Hubbard Model with the fRG

The DMF2RG has been introduced to overcome the weak-coupling limitation of the fermionic functional renormalization group (fRG). This approach builds on the idea to exploit the dynamical mean-field theory (DMFT) as starting point for the fRG flow, thus capturing local nonperturbative correlations via DMFT together with perturbative nonlocal correlations generated during the flow. We show how nonlocal nonperturbative correlations can be also incorporated in the DMF2RG scheme by using cellular DMFT (CDMFT) for a 2×2 cluster instead of single-site DMFT as starting point of the flow. Both CDMFT and fRG implementations have been formulated within the single-boson exchange decomposition, which has already proven to be an insightful bosonization scheme. We illustrate the ability of this novel approach to efficiently capture nonlocal nonperturbative correlations in the 2d Hubbard model.

Speaker: Marcel Krämer

14:30 U(1) Gauge-Field-Driven Non-Fermi Liquids: The Functional Renormalization Group and Symmetries

Developing a predictive theory of non-Fermi liquids (NFLs) in two spatial dimensions remains a key challenge to modern condensed matter physics. At the level of real materials, it could provide insight into such pressing problems as high-T_c superconductivity, while in the abstract it is paradigmatic of the poorly understood scenario of 2-D criticality induced by a gapless boson interacting with finite density fermions. The functional renormalization group is particularly appropriate for studying NFLs, as it can handle the strong interactions and non-analytic operators inherent to them [1,2] – however, due to the breakdown of the quasiparticle picture, little is known about the form of the low-energy field theory and most theoretical approaches suffer a lack of predictive power. We seek to remedy this by using known exact identities, such as those provided by symmetries, to constrain the modelling. Specifically, we nonperturbatively study the problem of a U(1) gauge-field interacting with a 2-D Fermi-surface; it has long been known that the magnetic vector potential is not screened by the particle-hole continuum and so induces criticality [3,4]. We first show how the choice of regulators interplays with the U(1) symmetry – in particular, in order to correctly capture Landau-damping we need a soft frequency regulator for the fermions, which breaks the gauge symmetry and leads to modified Ward identities. These identities, though less tractable than the standard Ward identities, still provide exact relations between the couplings and constrain the flow. We discuss the NFL fixed point hosted by the model, and demonstrate how incorporation of the modified Ward identities influences its properties. We finish with some commentary on UV-IR mixing induced in the low energy physics by gauge symmetry, and the implications our results have for predictive modelling of non-Fermi liquids. [1] S. A. Maier and P. Strack, Phys. Rev. B 93, 165114 (2016) [2] W. Metzner, M. Salmhofer, C. Honerkamp, V. Meden and K. Schönhammer, Rev. Mod. Phys. 84, 299 (2012) [3] M. Yu. Reizer, Phys. Rev. B 40, 11571 (1989) [4] S. Chakravarty, R. E. Norton and O. F. Syljuåsen, Phys. Rev. Lett. 74, 1423 (1995)

Speaker: Thomas Sheerin

14:30 UV conformal window of 4d gauge theories with matter

Using RG methods, I study the UV conformal window of weakly coupled gauge theories weakly with matter. Using beta functions up to four-loop in perturbation theory, I discuss results for fixed points and scaling dimensions as power series in a small Veneziano parameter. Particular emphasis is put on the mechanism resonsible for the end of the conformal window, and a competition between the loss of vacuum stability and potential merger in the gauge or the double-trace scalar sectors. The study is largely based on 2307.08747 and forthcoming work.

Speakers: Daniel Litim, Nahzaan Riyaz

14:30 Walking, Nordic Walking, and Deconfined Pseudocriticality

Not all possible phase transitions occurring in nature are captured by the Landau-Ginzburg-Wilson-Fisher paradigm. An exciting class of such non-Landau transitions are deconfined quantum critical points (DQCP) which exhibit emergent fractional excitations and gauge fields at criticality. The primary example in the study of DQCPs has been a system of half-integer spins on a square lattice with competing interactions. Whether or not this system shows true criticality, however, is a major open question in the field. In fact, numerical simulations for this model either indicate weak-first order behavior or at least a severely anomalous continuous transition between Néel and valence bond solid order. In my contribution, I will explain how weak first-order behaviour manifests itself during a renormalisation group flow. Furthermore, I will discuss effective field theories pertinent to DQCPs such as the (2+1)-dimensional SO(5) Wess-Zumino-Witten theory and the N-component Abelian Higgs model utilising a functional renormalisation group approach based on higher-order regulators and show how walking and nordic walking can appear in these theories.

Speaker: Bilal Hawashin

16:10 → 16:40 Break

16:40 → 18:00 Parallel A

16:40 Effective field theory at nuclear scales from the functional renormalization group

The atomic nucleus is a complex system : it is made of composite degrees of freedom strongly coupled by their (strong and electroweak) interactions and hosts a bunch of emergent behaviors, e.g. deformations as well as superfluid and molecular instabilities. Nuclear structure physics endeavors a robust and accurate description of the way an arbitrary number of nucleons self-organizes and gets disorganized in nuclei. To achieve this goal, nuclear physics has entered an era of reformulation of its standard phenomenological models into bona fide effective field theories (EFTs). However, the empirical microscopic model offering the best compromise between predictive power and numerical complexity - the so-called energy density functional (EDF) - has so far resisted all attempts of reformulation into an EFT. In this talk, we show that the functional renormalization group is the appropriate tool for tuning the EDF into an EFT.

Speaker: Jean Paul Ebran

Ebran-Heitz_ERG2024.pdf

17:10 Dynamic Criticality and Dissipation in Model A

In this talk, I will explore the dissipation rate of a scalar field near the phase transition and within the ordered phase, focusing on systems that fall under the universality class of Model A. Our approach employs a dynamical field theory framework, where we perform a leading-order expansion of the effective action in terms of field gradients while retaining full field dependence. I will present the solution of functional renormalization group (fRG) equations to determine both the effective potential and the dissipation rate. Of particular interest are the static and dynamic critical behaviors, as well as the symmetry-broken phase. In the latter, we observe that the transport coefficient of the dissipative fluid equation acquires a barrier that grows exponentially with system volume. Additionally, I will outline the process of computing the ansatz for the effective action within the fRG formalism in real time, extending the analysis up to second-order field derivatives.

Speaker: Laura Batini

17:40 New Results for Reggeons using FRG and Wilson Regularization and ε – expansion

In this talk we extend our recent non perturbative functional renormalization group analysis of Reggeon Field Theory to the interactions of Pomeron/Odderon fields and two Pomeron fields. We establish the existence of a fixed point and its universal properties. This analysis, allows to connect the nonperturbative infrared region (large transverse distances) with the UV region of small transverse distances where the high-energy limit of perturbative QCD applies. We discuss the implications of result for the existence of an Odderon in high-energy scattering.

Speaker: Carlos Contreras

CONTRERAS-ERG2024f.pdf

16:40 → 18:00 Parallel B

16:40 Local 2PI vertex approximation: Nanoflakes, ferromagnets, and SU(2) gauge theory for antiferromagnets

I discuss application of local 2PI Vertex Approximation (also known as a coupled ladder approximation) to description of charge, spin instabilities in graphene nanoflakes, as well as spin instabilities in magnetic systems. In graphene nanoflakes for strong on-site repulsion the spin density wave instability is obtained, while for strong non-local interaction the charge density wave instability occurs. For bare Coulomb interaction the boundaries of instabilities are in good agreement with quantum Monte-Carlo method. At the same time, realistic screening of Coulomb interaction strongly suppresses charge density wave instability. For magnetic systems with fcc lattice we obtain doping dependence of Curie temperature. The used approximation and its results are related and compared to those of dynamical mean-field theory.

Speaker: Andrey Katanin

17:10 The zoo of states in the 2D Hubbard model

We use a combination of real-space Hartree-Fock theory and functional renormalization group to unbiasedly construct a phase diagram of the 2D Hubbard model in Temperature and Doping. We are able to detect various spin- and charge order patterns including Néel, stripe and spiral order. I will give a short summary of the method followed by a presentation of our current results and a possible outlook for further applications.

Speaker: Robin Scholle

17:40 Full potential approach to frustrated antiferromagnets

We revisit the critical behavior of classical frustrated systems using the nonperturbative renormalization group (NPRG) equation. Our study is performed within the local potential approximation of this equation to which is added the flow of the field renormalization. Our flow equations are functional to avoid possible artifacts coming from field expansions which consists in keeping only a limited number of coupling constants. The function $N_c(d)$ separating the regions of first and second order in the $(d,N)$ plane is computed for $d$ between 4 and 2.5. Our results are compared with both the fixed dimension perturbative approach and the results obtained within the conformal bootstrap approach.

Speaker: Shunsuke Yabunaka

ERG2024-Yabunaka.pdf

19:00 → 20:00 Dinner

Wednesday 25 September

09:00 → 09:40 Critical Dynamics and Non-Equilibrium Phase Transitions in QCD

Speaker: Lorenz von Smekal (Justus-Liebig University Giessen)

LvS_Sept_2024.pdf

09:40 → 10:20 Some result of critical dynamics of the O(4) critical point in QCD

Speaker: Eduardo Grossi

ERG-Grossi.pdf

10:20 → 11:00 Universal location of Yang-Lee edge singularity with Functional RG

Speaker: Vladimir Skokov

Online Slides

11:00 → 11:30 Break

11:30 → 12:10 Low-energy effective theories of metals

The fixed points of the renormalization group flow are crucial for classifying phases of matter and understanding their universal low-energy physics. In metals, however, fixed points are defined only projectively due to the indefinite growth of Fermi momentum under scale transformations. In this talk, I will discuss the physical implications of the projective nature of metallic fixed points and the recent progress made in charting the space of universality classes for non-Fermi liquids.

Speaker: Sung-Sik Lee

ERG2024.pdf

12:10 → 12:50 UV complete field theory in (2+1)D with symmetry breaking at all temperatures

It was recently established that spontaneous symmetry breaking can persist at all temperatures in certain biconical $\mathrm{O}(N)\times \mathbb{Z}_2$ vector models when the underlying field theories are asymptotically safe. So far, the existence of such models has only been explored in fractional dimensions for local but non-unitary models or in 2+1 dimensions but for non-local models. In my talk, I will discuss our study of local models at zero and finite temperature directly in 2+1 dimensions employing functional methods. At zero temperature, I show that our approach reproduces the critical behaviour with high accuracy for all $N\geq 2$. I will then exhibit the mechanism of discrete symmetry breaking from $\mathrm{O}(N)\times \mathbb{Z}_2\to \mathrm{O}(N)$ for increasing temperature near the biconical critical point when $N$ is finite but large. We calculated the corresponding full finite-temperature phase diagram and further showed that the Mermin-Wagner-Hohenberg theorem is respected within this approach, i.e., symmetry breaking only occurs in the $\mathbb{Z}_2$ sector. Finally, we also determined the critical value of $N$ above which this phenomenon occurs to be $N_c \approx 15$.

Speaker: Michael Scherer

SchererERG2024.pdf

12:50 → 14:30 Lunch

14:30 → 15:50 Parallel A

14:30 Synergies between UV-safety and model building

I report on recent developments in model building and flavor phenomenology that is using RG-techniques and UV-safety.

Speaker: Gudrun Hiller (Technische Universitaet Dortmund (DE))

synergies-UV-modelbuilding-ghiller2024.pdf

14:50 Conformality, dynamical chiral symmetry breaking and confinement: interplay and cartography of gauge-fermion dynamics

We study the interplay of colour confinement and dynamical symmetry breaking dynamics in gauge theories coupled to fermions. We provide a first-principles analysis employing the functional Renormalisation Group. We analyse the landscape of theories spanning from QCD-like to the conformal window, showing evidence for walking dynamics. Employing bosonisation techniques we access fundamental properties of the strongly coupled theories such as the relation between fundamental scales, the chiral condensate and the constituent fermion masses. Last we provide a quantitative estimate for the lower boundary of the conformal window.

Speaker: Álvaro Pastor Gutiérrez

ERG_PastorGutierrez_9_24.pdf

15:10 Functional renormalisation of UV-safe gauge theories coupled to matter

Certain types of large-$N$ gauge theories coupled to matter offer interacting UV fixed points that are under strict perturbative control, beyond the paradigm of asymptotic freedom. In this work, we derive and investigate functional RG equations for the quantum effective potential of the theory to leading order in a derivative expansion. We thereby find the RG flows, fixed points, and scaling dimensions of infinitely many canonically irrelevant interaction monomials to leading order in the small Veneziano parameter. We also find that results can be resummed into closed expressions. Implications for vacuum stability and the size of the conformal window, links with RG studies in the MS bar scheme, and extensions towards larger Veneziano parameters are indicated.

Speaker: Daniele Rizzo (NCBJ)

Rizzo_Daniele.pdf

15:30 From fluctuating gravitons to Lorentzian quantum gravity and scattering amplitudes

Over the past decades, the asymptotic safety scenario has matured into a viable contender for a consistent theory of quantum gravity. Recently, the existence of a fixed point and a well-behaved graviton propagator were for the first time confirmed in a direct Lorentzian computation based on running spectral functions. I will detail the latest results in the computation of graviton spectral functions, which leads to the first results for form factors of the quantum effective action and graviton-mediated scattering amplitudes. All results obtained are compatible with the unitarity of asymptotically safe gravity. I will compare the results to theories that are asymptotically safe but perturbatively renormalisable.

Speaker: Manuel Reichert

ERG.pdf

14:30 → 15:50 Parallel B

14:30 Bosonization for fermionic fRG at weak and strong couplings

The vertex expansion of the Wetterich equation provides a reliable perturbative approach for purely fermionic systems, already at the 1-loop level. The conventional 1-loop truncation can be improved by means of the multiloop functional renormalization group (fRG) which relies on flow equations derived from self-consistent equations for the flowing vertices (Bethe-Salpeter equation, …). The heart of this work is a bosonization technique called single-boson exchange (SBE) formalism, which allows for introducing bosonic couplings through an efficient decomposition of the fermionic two-particle vertex. In this talk, I will illustrate how this SBE approach makes the fermionic multiloop fRG scheme more insightful and more tractable by discussing applications to the 2D Hubbard model. Extensions to strong couplings using correlated starting points for the fRG flow will be discussed as well.

Speaker: Kilian Fraboulet

Fraboulet_ERG2024.pdf

14:50 Single-boson exchange formulation of the Schwinger-Dyson equation and its application to the fRG

We extend the recently introduced single-boson exchange (SBE) formulation to the computation of the self-energy from the Schwinger-Dyson equation. In particular, we derive its general expression both in diagrammatic and in physical channels and show that the SBE formulation of the Schwinger-Dyson equation can be naturally applied also to non-local interactions. We furthermore discuss its implications in a truncated unity solver. As an application, we provide fRG results for the two-dimensional Hubbard model at weak coupling, where the use of the Schwinger-Dyson equation for the self-energy flow allows to capture the pseudogap opening. We illustrate that the SBE formulation proves particularly advantageous in identifying the relevant physical channels that drive the physical behavior. The expressions obtained for the self-energy rely on a single-channel parametrization, allowing further investigations within a fluctuation diagnostic of the different self-energy contributions, and this would enable to establish a comprehensive framework applicable to models with a non-local interaction or an $SU(2)$ symmetry broken phase. We discuss the extension to the strong coupling regime by combining the fRG with dynamical mean-field theory (DMFT) in the so-called DMF2RG.

Speaker: Miriam Patricolo

15:10 The role of quenched disorder in polymerized membranes

I review recent studies aiming to understand the effects of quenched disorder on polymerized membranes. This concerns both the ordered - flat - phase of membranes that is relevant for graphene and graphene-like materials and the crumpled-to-flat transition that takes place in generic polymerized membranes. I show that perturbative together with nonperturbative approaches provide a unified view of the phenomena taking place in these systems and reveal some intriguing behaviours.

Speaker: Dominique Mouhanna

ERG2024.pdf

15:30 Generalized Hertz action for quantum criticality in Fermi systems

We reassess the structure of the effective action and quantum critical singularities of two-dimensional Fermi systems characterized by the ordering wavevector Q⃗=0⃗. By employing infrared cutoffs on all the massless degrees of freedom, we derive a generalized form of the Hertz action, which does not suffer from problems of singular effective interactions. We demonstrate that the Wilsonian momentum-shell renormalization group (RG) theory capturing the infrared scaling should be formulated keeping Q⃗ as a flowing, scale-dependent quantity. At the quantum critical point, scaling controlled by the dynamical exponent z=3 is overshadowed by a broad scaling regime characterized by a lower value of z≈2. This in particular offers an explanation of the results of quantum Monte Carlo simulations pertinent to the electronic nematic quantum critical point.

Speaker: Pawel Jakubczyk

ERG_2024-Jakubczyk.pdf

15:50 → 16:20 Break

16:20 → 18:00 Parallel A

16:20 Entanglement in an expanding universe

I discuss the evolution of entanglement entropy for a massless field within a spherical region in an expanding background. The formalism is applied to the inflationary period and the subsequent era of radiation domination, starting from the Bunch-Davies vacuum. Each field mode evolves towards a squeezed state upon horizon exit during inflation, with additional squeezing when radiation domination sets in. This results in the enhancement of the entanglement entropy. A volume term develops in the radiation-dominated era, and becomes the leading contribution to the entropy at late times. I discuss the interpretation of the entropy in the light of the quantum to classical transition for modes exiting the horizon during inflation. Entranglement could be a means to track the quantum origin of weakly interacting fields, such as gravitational waves resulting from tensor modes during inflation. On the other hand, an observer with no knowledge of the degrees of freedom beyond the horizon would interpret the entropy as thermal. From this point of view, the reheating after inflation would be a result of quantum entanglement. I present results on the precise expression for the entropy in de Sitter space. I also speculate on the possibility to check these results in analogue gravity experiments.

Speaker: Nikolaos Tetradis (National and Kapodistrian University of Athens (GR))

Entanglement-Tetradis.pdf

16:50 Order of the SU(N_f) x SU(N_f) chiral transition

Renormalization group flows of the Ginzburg-Landau potential of chiral symmetry restoration are calculated for a general number of quark flavors (N_f), with the inclusion of all possible (perturbatively) relevant and marginal operators in d = 3 spatial dimensions. We find new, potentially infrared stable fixed points spanned throughout the entire N_f range. By conjecturing that the thermal chiral transition is governed by these ``flavor continuous" fixed points, stability analyses show that for N_f >= 5 the chiral transition is of second-order, while for N_f =2,3,4, it is of first-order. We argue that the U_A(1) anomaly controls the strength of the first-order chiral transition for N_f = 2,3,4, and makes it almost indistinguishable from a second-order one, if it is sufficiently weak at the critical point. This could open up a new strategy to investigate the strength of the U_A(1) symmetry breaking around the critical temperature.

Speaker: Gergely Fejos (Eötvös University Budapest)

fejos.pdf

17:20 Strangeness neutrality and QCD phase structure from functional renormalization group

We improve the $N_f=2+1$ QCD theory within the functional renormalization group (fRG) approach at finite temperature and chemical potential. Starting from the gluon and quark degrees of freedom in the perturbative high-energy regime, we systematically integrate out quantum fluctuations towards the mesons and baryons degrees of freedom in the low-energy regime with dynamical hadronization. The strange quark and the nonets of scalar and pseudoscalar mesons are self-consistent included. The light quark chiral condensate and the reduced condensate are quantitatively in agreement with the lattice QCD results. Besides, the second order fluctuations and correlation of baryon number and strangeness, i.e. $\chi^B_2$, $\chi^S_2$ and $\chi^{BS}_{11}$ are also calculated and comparable with the lattica results. The QCD phase structure is given with constraints $\mu_S=0$ and $n_S=0$.

Speaker: Rui Wen

Strangeness neutrality and QCD phase structure from functional (1) (1).pdf

17:40 Universal critical dynamics in QCD

In this talk, I will give an overview of the universal critical dynamics at the chiral phase transition of two-flavor QCD in the chiral limit. I will review the argument by Rajagopal and Wilczek of the associated dynamic universality class being "Model G" from the Halperin-Hohenberg classification. To extract dynamic universal quantities, we use a novel formulation of the functional renormalization group for dynamical systems with "reversible mode couplings". I will show results for dynamic universal quantities such as the non-trivial value z=d/2 of the dynamic critical exponent at the "strong-scaling" fixed point (where d is the number of spatial dimensions) and for dynamic universal scaling functions. Finally, I will outline how the same method can be used to study the universal dynamics at the QCD critical point, with the dynamic universality class being "Model H" in this case.

Speaker: Johannes Roth

ERG2024Roth.pdf

16:20 → 18:00 Parallel B

16:20 Secondary instabilities of 2D altermagnets

We explore the possible weak coupling instabilities of the 2D Hubbard model with existing altermagnetic order, within a truncated unity functional renormalization group (tUfRG) framework. We find that as a function of chemical potential the system exhibits instabilities towards distinct SDW orders that coexist with the altermagnetic order. We also find that the system exhibits superconducting instabilities for several parameter regimes.

Speaker: Nikolaos Parthenios

16:50 Accurate estimates of universal quantities: Monte Carlo simulations of improved lattice models and finite size scaling

The accurate determination of universal quantities, such as critical exponents,
by using high temperature series expansions or Monte Carlo simulations of
lattice models is hampered by corrections to scaling.
In [J. H. Chen, M. E. Fisher and B. G. Nickel, Phys. Rev. Lett. 48, 630 (1982)]
the authors suggested to study one parameter families of models.
The amplitudes of corrections to scaling depend on the parameter of the model
family. In the case of the Ising universality class in three dimensions a zero
of the amplitude of the leading correction can be found. Starting from the
nineties of the last century, this idea has been expoited by using Monte
Carlo simulations in conjunction with finite size scaling.
I sketch the basic ideas and summarize numerical results for the Ising, the
XY and the Heisenberg universality classes in three dimensions.
Recently I have studied the cubic fixed point in three dimensions. I obtain
y_t,cubic − y_t,O(3) = 0.00124(12) for the difference of the thermal
RG-exponents of the cubic and the O(3) invariant fixed points in three
dimensions.

Speaker: Martin Hasenbusch

17:20 Phase diagram of the J1-J2 quantum Heisenberg model for arbitrary spin

We use the spin functional renormalization group to investigate the J1-J2 quantum Heisenberg model on a square lattice. By incorporating sum rules associated with the fixed length of the spin operators as well as the nontrivial quantum dynamics implied by the spin algebra, we are able to compute the ground state phase diagram for arbitrary spin S, including the quantum paramagnetic phase at strong frustration. Our prediction for the extent of this paramagnetic region for S = 1/2 agrees well with other approaches that are computationally more expensive. We find that the quantum paramagnetic phase disappears for S > 5 due to the suppression of quantum fluctuations with increasing S.

Speaker: Andreas Rückriegel

talk_erg12_rueckriegel.pdf

17:40 The inviscid fixed point of the multi-dimensional Burgers-KPZ equation

A new scaling regime characterized by a $z=1$ dynamical critical exponent has been reported in several numerical simulations of the one-dimensional Kardar-Parisi-Zhang and noisy Burgers equations [1]. This scaling was found to emerge in the tensionless limit for the interface and in the inviscid limit for the fluid. Based on functional renormalization group, the origin of this scaling has been elucidated [2]. It was shown to be controlled by a yet unpredicted fixed point of the one-dimensional Burgers-KPZ equation, termed inviscid Burgers fixed point. The associated universal properties, including the scaling function, were calculated. In the present work, we generalize this analysis to the multi-dimensional Burgers-KPZ equation [3]. We show that the inviscid-Burgers fixed point exists in all dimensions $d$, and that it controls the large momentum behavior of the correlation functions in the inviscid limit. It turns out that it yields in all $d$ the same super-universal value $z=1$ for the dynamical exponent. [1] C. Cartes, E. Tirapegui, R. Pandit, M. Brachet, Phil. Trans. Roy. Soc. A 380, 20210090 (2022); E. Rodriguez-Fernandez, S. N. Santalla, M. Castro, R. Cuerno, Phys. Rev. E 106, 024802 (2022); K. Fujimoto, R. Hamazaki, Y. Kawaguchi, Phys. Rev. Lett. 124, 210604 (2020). [2] C. Fontaine, F. Vercesi, M. Brachet, L. Canet, Phys. Rev. Lett. 131, 247101 (2023). [3] L. Gosteva, M. Tarpin, N. Wschebor, L. Canet, submitted, arxiv.org/abs/2406.14030.

Speaker: Liubov Gosteva

Gosteva L erg2024_3-3.pdf

19:00 → 20:00 Dinner

Thursday 26 September

09:00 → 09:40 Symmetric improved estimators for multipoint vertex functions

Multipoint vertex functions, and the four-point vertex in particular, are crucial ingredients in many-body theory. Recent years have seen significant algorithmic progress toward numerically computing their dependence on multiple frequency arguments. However, such computations remain challenging and are prone to suffer from numerical artifacts, especially in the real-frequency domain. Here, we derive estimators for multipoint vertices that are numerically more robust than those previously available. We show that the two central steps for extracting vertices from correlators, namely, the subtraction of disconnected contributions and the amputation of external legs, can be achieved accurately through repeated application of equations of motion, in a manner that is symmetric with respect to all frequency arguments and involves only fully renormalized objects. The symmetric estimators express the core part of the vertex and all asymptotic contributions through separate expressions that can be computed independently, without subtracting the large-frequency limits of various terms with different asymptotic behaviors. Our strategy is general and applies equally to the Matsubara formalism, the real-frequency zero-temperature formalism, and the Keldysh formalism. We demonstrate the advantages of the symmetric improved estimators by computing the Keldysh four-point vertex of the single-impurity Anderson model using the numerical renormalization group.

Speaker: Jan von Delft

vonDelft.pdf

09:40 → 10:20 Different flavours of fermion quadrupling condensates in magic-angle twisted bilayer graphene

Magic-Angle Twisted Bilayer Graphene is shown to host a large variety of interesting states of matter, including an unconventional superconducting state. 
But could this material form completely new states of matter? 

In this talk, I will discuss the possible emergence of two different types of electron condensates that go beyond the BCS coupling paradigm. These are condensates formed by fermionic quadruplets exhibiting no phase coherence between pairs of electrons, but between pairs of pairs.
By employing large-scale Monte Carlo simulations on a low-energy effective model [1] for magic-angle twisted-bilayer graphene, we show that depending on the superconducting ground state, fermion quadrupling condensates may emerge as vestigial phases.

More specifically, we find that if the ground state is a superconductor additionally breaking time-reversal symmetry, a condensate formed by four electrons which breaks time-reversal symmetry generically emerges above the superconducting transition [2]. Conversely, if the ground state is a nematic superconductor, our numerical simulations show that the system exhibits a charge-4e phase before melting in the normal metal phase [3].
This indicates that twisted bilayer graphene is an ideal platform to stabilise and observe these novel quantum states.

[1] D. V. Chichinadze, L.Classen, and A. V. Chubukov Phys. Rev. B 101, 224513 (2020);
[2] I. Maccari, J. Carlström, E. Babaev, Phys. Rev. B 107 (6), 064501 (2023).
[3] I. Maccari, J. Carlström, E. Babaev, In Preparation.

Speaker: Ilaria Maccari

ERG2024_IMPresentation.pdf

10:20 → 11:00 Diagrammatic approach to quantum spin systems

Frustrated quantum spin systems remain challenging to treat with state-of-the-art numerical methods. We review our recent fRG approach based on a pseudo-Majorana representation. We then turn to a rarely-applied diagrammatic formulation in terms of spin operators dating back to the 1960s. We pair this approach with modern computational capabilities and consider applications from the quantum optical community. We show that the resulting predictions for magnetic phase boundaries are surprisingly accurate. We also shed new light on a puzzling correspondence between spatial spin correlation patterns of quantum and classical spins where the latter are evaluated at a slightly elevated temperature.

Speaker: Björn Sbierski

11:00 → 11:30 Break

11:30 → 12:10 Running couplings in quadratic gravity

One can define running couplings in various ways, some of which have a more immediate physical meaning. I will illustrate this in some scalar models and in quadratic gravity.

Speaker: Roberto Percacci (SISSA)

diablerets.pdf

12:10 → 12:50 Gradient Flow Exact Renormalization Group

I am going to review a formulation of the exact renormalization group that reproduces gradient flows introduced earlier by Luescher. So far it has been successfully applied to QED. Applications to non-abelian gauge theories are for the future.

Speaker: Hidenori Sonoda

sonoda-erg2024.pdf

12:50 → 14:30 Lunch

14:30 → 15:50 Parallel A

14:30 Analytic solutions for scaling dimensions of highly irrelevant operators in LPA and f(R) approximations

We show that in the local potential approximation of the functional renormalization group, and in the f(R) approximation to asymptotically safe gravity, a combination of Sturm-Liouville and WKB methods allows for an exact analytical solution for scaling dimensions of highly irrelevant operators. The results shed light on properties of these approximations and in particular on recent numerical evidence of almost Gaussian scaling in the f(R) approximation and the extent to which these results are (non)universal.

Speaker: Tim Morris (Southampton University)

ERG2024.pdf

14:50 Wavelet view on the Landau poles in quantum field theory

Following the paper M. Altaisky Phys. Rev. D 93 (2016) 105043, we develop a new approach to the renormalization group, where the effective action functional $\Gamma_A[\phi]$ is a sum of all fluctuations of scales from the size of the system ($L$) down to the scale of observation ($A$). It is shown that the renormalization flow equation of the type $ \frac{\partial \Gamma_A}{\partial \ln A} = X(A) $ is a limiting case of such consideration, when the running coupling constant is assumed to be a differentiable function of scale. In this approximation, the running coupling constant, calculated at one-loop level, suffers from the Landau pole. In general case, when the scale-dependent coupling constant is a non-differentiable function of scale, the Feynman loop expansion results in a difference equation. This keeps the coupling constant finite for any finite value of scale $A$. As an example we consider the Euclidean $\phi^4$ field theory. The talk is based on the recent paper M.Altaisky and M.Hnatich, Phys. Rev. D 108 (2023)085023.

Speaker: Mikhail Altaisky

Altaisky2024ERG.pdf

15:10 Asymptotic Safety in Generalized Proca Theories

There are still many unanswered questions from General Relativity, such as black holes singularity and dark energy: these puzzles have led to the development of extended theories of gravity. One approach to modifying General Relativity consists of adding new degrees of freedom, such vector fields, resulting in the so-called Generalized Proca theories. In order to determine whether these theories are consistent and can provide predictions, this work investigates the possibility of an “asymptotically safe” ultraviolet completion, which would make them free from unphysical ultraviolet divergences. This involves analyzing their beta functions and establishing whether there exist fixed points acting as partial ultraviolet attractors.

Speaker: Sara Rufrano Aliberti

ERG24_RufranoAliberti.pdf

15:30 Essential Renormalization Group Equation for Gravity coupled to Scalar Matter

In the renormalization group approach, it is known that inessential
couplings could be removed by the field redefinitions. Recently it is
pointed out that the quadratic curvature terms fall into this class of
operators, and next cubic term is irrelevant. This suggests that the
Einstein and cosmological term is enough to define asymptotically safe
quantum gravity for pure gravity. Here we extend the study to the case
when the matter is present.

Speaker: Nobuyoshi Ohta (Kinki University)

ERG2024_ohta.pdf

14:30 → 15:50 Parallel B

14:30 Recursive algorithm for generating high-temperature expansions for spin systems and the chiral non-linear susceptibility

We show that the high-temperature expansion of the free energy and arbitrary connected correlation functions of quantum spin systems can be recursively obtained from the exact renormalization group flow equation for the generating functional of connected spin correlation functions derived by Krieg and Kopietz [Phys. Rev. B 99, 060403(R) (2019)]. Our recursive algorithm can be explicitly written down in closed form including all combinatorial factors. We use our method to estimate critical temperatures of Heisenberg magnets from low-order truncations of the inverse spin susceptibility in the static limit. We also calculate the connected correlation function involving three different spin components (chiral non-linear susceptibility) of quantum Heisenberg magnets up to second order in the exchange couplings.

Speaker: Peter Kopietz

talk_ERG12_kopietz.pdf

14:50 Quantum effects on unconventional pinch-point singularities from pseudo-fermion functional renormalization

The discovery of emergent gauge theories in condensed matter systems is associated with novel phenomena such as fractionalization and topological excitations. A prime example are spin ice compounds, which are materials hosting a ground state described by an emergent U(1) gauge theory, featuring monopole excitations arising from the fractionalization of microscopic spin degrees of freedom. Remarkably, signatures of the gauge structure are visible in neutron scattering measurements as pinch-point singularities. Recently, classical spin liquids on the pyrochlore lattice have been proposed with a higher-rank gauge structure, where instead of a conventional gauge field the low- energy physics is described by fluctuations of a tensor field with a continuous gauge freedom. The corresponding classical correlations show variations of the conventional pinch-point singularities, such as pinch-lines or multi-fold pinch-points. Here, we investigate the effect of quantum fluctuations on these signatures using a state-of-the-art implementation of the pseudo-fermion functional renormalization group approach. We observe a significant modification of the signal drastically different from the simple broadening due to thermal fluctuations, highlighting the importance of quantum fluctuations in possible material realizations and interpretation of experimental observations.

Speaker: Lasse Gresista

15:10 Real-frequency quantum field theory applied to the single-impurity Anderson model

A major challenge in the field of correlated electrons is the computation of dynamical correlation functions. For comparisons with experiment, one is interested in their real-frequency dependence. This is difficult to compute because imaginary-frequency data from the Matsubara formalism require analytic continuation, a numerically ill-posed problem. Here, we apply quantum field theory to the single-impurity Anderson model using the Keldysh instead of the Matsubara formalism with direct access to the self-energy and dynamical susceptibilities on the real-frequency axis. We present results from the functional renormalization group (fRG) at the one-loop level and from solving the self-consistent parquet equations in the parquet approximation. In contrast with previous Keldysh fRG works, we employ a parametrization of the four-point vertex which captures its full dependence on three real-frequency arguments. We compare our results to benchmark data obtained with the numerical renormalization group and to second-order perturbation theory. We find that capturing the full frequency dependence of the four-point vertex significantly improves the fRG results compared with previous implementations, and that solving the parquet equations yields the best agreement with the numerical renormalization group benchmark data but is only feasible up to moderate interaction strengths. Our methodical advances pave the way for treating more complicated models in the future.

Speaker: Nepomuk Ritz

2024ERG_NepomukRitz.pdf

15:30 divERGe - an open source functional renormalization code for material calculations

We present divERGe, an open source, high-performance C/C++/Python library for functional renormalization group (FRG) calculations on lattice fermions. The versatile model interface is tailored to real materials applications and seamlessly integrates with existing, standard tools from the ab-initio community. The code fully supports multi-site, multi-orbital, and non-SU2 models in all of the three included FRG variants: TUFRG, N-patch FRG, and grid FRG. In this talk I will give a short overview of the interface and present results from different material calculations.

Speaker: Jonas Profe

15:50 → 17:20 Free time for discussions

19:00 → 20:00 Fondue Dinner

Friday 27 September

09:00 → 09:40 Asymptotic Safety Landscapes at the intersection between Positivity Bounds and Swampland Conjectures

I will review recent progress in computing and analyzing the "landscape" of effective field theories stemming from an asymptotically safe ultraviolet completion of gravity. I will argue that this is an essential task in asymptotic safety, as well as in other approaches to quantum gravity, to test their consistency and to facilitate the comparison between their predictions. Concretely, I will focus on purely gravitational and gravity-photon systems, and I will discuss the intersections between the resulting asymptotic safety landscape, the string landscape identified by (some) swampland constraints, and positivity bounds.

Speaker: Alessia Platania

09:40 → 10:20 O(3) Nonlinear Sigma Model and Non-Abelian Bosonization Duality

It is known that the SU(2) Wess-Zumino-Witten model is dual to the free fermion theory in two dimensions via non-Abelian bosonization. Additionally, the SU(2) Wess-Zumino-Witten model is believed to be equivalent to the O(3) nonlinear sigma model with the theta term. In this work, we reexamine this duality through the lens of renormalization group (RG) flow. We analyze the RG flow structure of the O(3) nonlinear sigma model with the theta term in two dimensions using the functional renormalization group. Our results reveal a nontrivial fixed point with a nonzero value of the topological coupling. The scaling dimensions (critical exponents) at this fixed point suggest the realization of duality between the O(3) nonlinear sigma model with the theta term and the free fermion theory, indicating that these models belong to the same universality class.

Speaker: Masatoshi Yamada

ERG2024-Yamada.pdf

10:20 → 11:00 Living on the edge: Quantum black hole physics from the event horizon

In this talk, I will employ a particle physics approach to uncover universal insights into the quantum properties of black holes. This framework will enable us to calculate thermodynamic quantities of the black hole, including the Hawking temperature and entropy, using model-independent expressions. I will also deduce general consistency conditions for the metric deformations. The approach is relevant for several applications ranging from a deeper understanding of the nature of the space and time to (astro) particle physics and cosmology. Finally, I will also suggest a novel way of testing Hawking Radiation via Black Hole morsels observations by atmospheric Cherenkov telescopes, opening the way of testing new high energy physics scenarios before the advent of the next generation colliders.

Speaker: Francesco Sannino (University of South Denmark (DK))

11:00 → 11:30 Break

11:30 → 12:10 When the RG must be functional and nonperturbative... Lessons from disordered systems

Speaker: Gilles Tarjus

Tarjus_ERG24.pdf

12:10 → 12:50 40 years of Polchinski's equation

Speaker: Manfred Salmhofer

12:50 → 14:30 Lunch