Phase structure of the massive chiral Gross-Neveu model from Hartree-Fock

TL;DR

This paper maps out the phase diagram of the massive chiral Gross-Neveu model in 1+1 dimensions using Hartree-Fock, revealing a chiral crystal phase, a Fermi gas phase, and critical points, with detailed analysis of phase transitions.

Contribution

It provides the first comprehensive phase diagram of the massive chiral Gross-Neveu model, including the identification of a chiral crystal phase and critical transition curves.

Findings

Identification of a chiral crystal phase separated by a first-order transition.

Construction of the critical sheet where homogeneous phase becomes unstable.

Mapping of the phase diagram as a function of fermion mass, chemical potential, and temperature.

Abstract

The phase diagram of the massive chiral Gross-Neveu model (the massive Nambu-Jona-Lasinio model in 1+1 dimensions) is constructed. In the large N limit, the Hartree-Fock approach can be used. We find numerically a chiral crystal phase separated from a massive Fermi gas phase by a 1st order transition. Using perturbation theory, we also construct the critical sheet where the homogeneous phase becomes unstable in a 2nd order transition. A tricritical curve is located. The phase diagram is mapped out as a function of fermion mass, chemical potential and temperature and compared with the one of the discrete chiral Gross-Neveu model. As a by-product, we illustrate the crystal structure of matter at zero temperature for various densities and fermion masses.