Inhomogeneous Phases in the Chiral Gross-Neveu Model on the Lattice

TL;DR

This study explores the phase structure of the 1+1 dimensional chiral Gross-Neveu model on the lattice, revealing the existence of an inhomogeneous phase at low temperature and high density, and analyzing chiral symmetry restoration.

Contribution

It provides the first lattice investigation of inhomogeneous phases in the chiral Gross-Neveu model at finite density and temperature.

Findings

Chiral symmetry is restored at high temperature.

Inhomogeneous phase exists at low temperature and high chemical potential.

Correlation functions clearly indicate inhomogeneous phase presence.

Abstract

We discuss possible existence of inhomogeneous phase in low temperature and high density region in the 1+1 dimensional chiral Gross-Neveu ( $\chi$GN$_2$ ) model on the lattice. First we investigate the phase structure of the $\chi$GN$_2$ model at vanishing chemical potential, changing temperature. From behavior of $\Delta^2 = \Sigma^2 + \Pi^2$ as a function of Monte Carlo time, a candidate of an order parameter for chiral symmetry in the $\chi$GN$_2$ model is $\Delta$. At vanishing chemical potential, we observe restoration of chiral symmetry at high $T$. In low temperature and high chemical potential region, we find existence of inhomogeneous phase in spatial correlation functions of $\sigma$ and $\pi$. The signal of inhomogeneous phase in correlation function of $\Delta$ is more clearly than that of $\sigma$ or $\pi$.