Phase Diagram of the Gross-Neveu Model: Exact Results and Condensed Matter Precursors

TL;DR

This paper analytically investigates the phase diagram of the large N Gross-Neveu model in 1+1 dimensions, revealing its structure and connections to condensed matter systems through exact solutions.

Contribution

It provides an exact analytical derivation of the phase diagram, linking relativistic quantum field theory results to condensed matter models.

Findings

Identified three phases: massless Fermi gas, massive Fermi gas, and kink-antikink crystal.

Mapped the Dirac-Hartree-Fock equation to a non-relativistic Schrödinger equation with Lame potential.

Established mathematical equivalence with phase diagrams in condensed matter physics.

Abstract

Recently the revised phase diagram of the (large N) Gross-Neveu model in 1+1 dimensions with discrete chiral symmetry has been determined numerically. It features three phases, a massless and a massive Fermi gas and a kink-antikink crystal. Here we investigate the phase diagram by analytical means, mapping the Dirac-Hartree-Fock equation onto the non-relativistic Schroedinger equation with the (single gap) Lame potential. It is pointed out that mathematically identical phase diagrams appeared in the condensed matter literature some time ago in the context of the Peierls-Froehlich model and ferromagnetic superconductors.