Inhomogeneous Condensates in the Thermodynamics of the Chiral NJL_2 model

TL;DR

This paper investigates the thermodynamics of the (1+1)-dimensional chiral NJL_2 model at finite density and temperature, revealing a thermodynamically favored chiral spiral phase through exact inhomogeneous condensate solutions.

Contribution

It provides a detailed analysis of inhomogeneous condensates in the NJL_2 model, highlighting the role of continuous chiral symmetry and identifying the chiral spiral as the preferred phase.

Findings

Chiral spiral is thermodynamically favored at finite density and temperature.

Inhomogeneous condensates are crucial for understanding the phase structure.

The study compares continuous and discrete chiral symmetry models.

Abstract

We analyze the thermodynamical properties, at finite density and nonzero temperature, of the (1+1)-dimensional chiral Gross-Neveu model (the NJL_2 model), using the exact inhomogeneous (crystalline) condensate solutions to the gap equation. The continuous chiral symmetry of the model plays a crucial role, and the thermodynamics leads to a broken phase with a periodic spiral condensate, the "chiral spiral", as a thermodynamically preferred limit of the more general "twisted kink crystal" solution of the gap equation. This situation should be contrasted with the Gross-Neveu model, which has a discrete chiral symmetry, and for which the phase diagram has a crystalline phase with a periodic kink crystal. We use a combination of analytic, numerical and Ginzburg-Landau techniques to study various parts of the phase diagram.