Speaker
Description
The phase diagram of finite-density QCD is potentially quite complex. Like other lattice models with sign problems and generalized $\mathcal PT$ symmetry, equilibrium states of lattice QCD at finite density may be inhomogeneous, with commensurate and incommensurate patterned phases. The phase structures of such models are determined by a set of interwoven concepts: $\mathcal PT$ symmetry, Lee-Yang zeros, violation of spectral positivity, Lifshitz instabilities, NP-hard complexity, and lattice duality. $\mathcal PT$ symmetry combined with lattice duality leads to models with removable sign problems in broad universality classes with rich phase structures. These models can be simulated on the lattice by standard techniques and analytical methods may be applied as well. These ideas are illustrated using models from the $i\phi^3$, $Z(2)$, $Z(3)$ and $SU(N)$ universality classes.
