From relativistic quantum fields to condensed matter and back again: Updating the Gross-Neveu phase diagram

TL;DR

This paper reviews recent revisions to the phase diagram of the large N Gross-Neveu model in 1+1 dimensions, highlighting its relevance to condensed matter systems and its role as a testing ground for new theoretical approaches.

Contribution

It provides a comprehensive update on the Gross-Neveu phase diagram, connecting relativistic quantum field theory with condensed matter phenomena and emphasizing its applications.

Findings

Revised phase diagram of the Gross-Neveu model at finite temperature and chemical potential.

Identification of the kink-antikink phase related to inhomogeneous superconductors.

The model's utility as a testing ground for new algorithms and theoretical ideas.

Abstract

During the last few years, the phase diagram of the large N Gross-Neveu model in 1+1 dimensions at finite temperature and chemical potential has undergone a major revision. Here we present a streamlined account of this development, collecting the most important results. Quasi-one-dimensional condensed matter systems like conducting polymers provide real physical systems which can be approximately described by the Gross-Neveu model and have played some role in establishing its phase structure. The kink-antikink phase found at low temperatures is closely related to inhomogeneous superconductors in the Larkin-Ovchinnikov-Fulde-Ferrell phase. With the complete phase diagram at hand, the Gross-Neveu model can now serve as a firm testing ground for new algorithms and theoretical ideas.