Inhomogeneous phases in the chirally imbalanced $2+1$-dimensional Gross-Neveu model and their absence in the continuum limit

TL;DR

This paper investigates the phase diagram of the 2+1D Gross-Neveu model with chiral imbalance, finding inhomogeneous phases at finite lattice spacing but not in the continuum limit, and relates chiral chemical potential to isospin imbalance.

Contribution

It demonstrates the absence of inhomogeneous phases in the continuum limit of the model and clarifies the equivalence between chiral and isospin chemical potentials.

Findings

Inhomogeneous phase observed at finite lattice spacing for one regularization.

No inhomogeneous phase in the continuum limit.

Chiral chemical potential is equivalent to isospin chemical potential.

Abstract

We study the $\mu$-$\mu_{45}$-$T$ phase diagram of the $2+1$-dimensional Gross-Neveu model, where $\mu$ denotes the ordinary chemical potential, $\mu_{45}$ the chiral chemical potential and $T$ the temperature. We use the mean-field approximation and two different lattice regularizations with naive chiral fermions. An inhomogeneous phase at finite lattice spacing is found for one of the two regularizations. Our results suggest that there is no inhomogeneous phase in the continuum limit. We show that a chiral chemical potential is equivalent to an isospin chemical potential. Thus, all results presented in this work can also be interpreted in the context of isospin imbalance.