Conveners
(DTP) M3-2 Quantum and Condensed Matter Theory | Théorie quantique et de la matière condensée (DPT)
- Manu Paranjape
We adapt a machine-learning approach to study the many-body localization transition in interacting fermionic systems on disordered 1D and 2D lattices. We perform supervised training of convolutional neural networks (CNNs) using labelled many-body wavefunctions at weak and strong disorder. In these limits, the average validation accuracy of the trained CNNs exceeds 99.95%. We use the...
The one-body density matrix (ODM) for a d-dimensional non-interacting Fermi gas can be approximately obtained in the semiclassical regime through different $\hbar$-expansion techniques. One would expect any method of approximating the ODM should yield equivalent density matrices which are both Hermitian and idempotent to any order in $\hbar$. The method of Grammaticos and Voros does ensure...
The Triamond lattice is the only maximally isotropic lattice where three links meet at each vertex, and for technical reasons, that provides an elegant bookkeeping method for quantum field theories on a lattice. Considering that until now, most researchers have not attempted to simulate Hamiltonians in three spatial dimensions, this work is an important step toward large-scale simulation on...
Analyzing the long term behaviour of solutions to a model gives insight on the physical relevance and numerical stability of the solutions. In our work, we consider the formulation presented by Blyth and Părău (2019), in which they derive the water-wave problem exclusively in terms of the free-boundary of a cylindrical geometry, and use it to solve for periodic travelling waves on the surface...
Dirac crystals are zero-bandgap semiconductors in which the valence and conduction bands are linear over the crystal momentum (and, therefore, non-dispersive) in the proximity of the Fermi level at the Brillouin zone boundary. They are therefore the quantum material analogue of the Dirac cone of light in special relativity. To understand a number of different properties of 2D Dirac crystals...
Rigorous derivations of the approach of individual elements of large isolated systems to a state of thermal equilibrium, starting from arbitrary initial states, are exceedingly rare. We demonstrate how, through a mechanism of repeated scattering, an approach to equilibrium of this type actually occurs in a specific quantum system.
In particular, we consider an optical mode passing through a...
