On the Inhomogeneous Phase of the Chiral Gross-Neveu Model

TL;DR

This paper demonstrates that the inhomogeneous chiral spiral phase in the 2d chiral Gross-Neveu model persists at finite N and zero temperature for any positive chemical potential, using non-abelian bosonization and diagrammatic methods.

Contribution

It provides a novel analysis showing the stability of the chiral spiral phase at finite N and zero temperature, and offers a simplified derivation of the phase diagram using non-abelian bosonization.

Findings

Chiral spiral phase persists at finite N and T=0 for all μ>0.

Non-abelian bosonization simplifies understanding of the inhomogeneous phase.

Agreement with previous large N phase diagram results.

Abstract

There is substantial evidence that the ground state of the 2d chiral Gross-Neveu model, in the presence of a $U(1)$ fermion number chemical potential $\mu$ and in the large $N$ limit, is given by a {\it chiral spiral} phase, namely an inhomogeneous phase with a chiral condensate having a spatially periodic phase. We show that the chiral spiral configuration persists at finite $N$ and $T=0$ for any $\mu>0$. Our analysis is based on non-abelian bosonization, that relates the model to a $U(N)_1$ WZW model deformed by current-current interactions. In this description the appearance of the inhomogeneous phase is surprisingly simple. We also rederive the phase diagram of the large $N$ chiral Gross-Neveu model via a direct diagrammatic computation, finding agreement with previous results in the literature.