On the Search for Inhomogeneous Phases in Fermionic Models

TL;DR

This paper investigates the phase diagram of the 1+1 dimensional Gross-Neveu model at finite temperature and chemical potential, introducing a fermion doubling method to efficiently identify inhomogeneous phases.

Contribution

The authors develop a fermion doubling technique that accurately predicts phase boundaries and the emergence of inhomogeneous ground states in the Gross-Neveu model.

Findings

Correctly predicts the boundary between symmetric and broken phases

Successfully identifies inhomogeneous ground states

Provides a method applicable to higher-dimensional fermionic models

Abstract

We revisit the Gross-Neveu model with N fermion flavors in 1+1 dimensions and compute its phase diagram at finite temperature and chemical potential in the large-N limit. To this end, we double the number of fermion degrees of freedom in a specific way which allows us to detect inhomogeneous phases in an efficient manner. We show analytically that this "fermion doubling trick" predicts correctly the position of the boundary between the chirally symmetric phase and the phase with broken chiral symmetry. Most importantly, we find that the emergence of an inhomogeneous ground state is predicted correctly. We critically analyze our approach based on this trick and discuss its applicability to other theories, such as fermionic models in higher dimensions, where it may be used to guide the search for inhomogeneous phases.