Phase structure of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin

TL;DR

This paper analyzes the phase diagram of the 1+1 dimensional Nambu--Jona-Lasinio model with isospin, revealing a novel crystalline phase and providing analytical solutions in the chiral limit, with stability analysis for the full phase diagram.

Contribution

It provides the first analytical solutions for the phase diagram with isospin in the NJL model and identifies a thermodynamically favored crystalline phase.

Findings

Discovery of a novel crystalline phase more stable than homogeneous phases at zero temperature.

Analytical solutions in the chiral limit expressed via known single-flavor models.

Construction of the phase boundary using stability analysis for the general case.

Abstract

The phase diagram of the two-dimensional Nambu--Jona-Lasinio model with isospin is explored in the large Nc limit with semiclassical methods. We consider finite temperature and include chemical potentials for all conserved charges. In the chiral limit, a full analytical solution is presented, expressed in terms of known results for the single-flavor Gross-Neveu and Nambu--Jona-Lasinio models. A novel crystalline structure appears and is shown explicitly to be thermodynamically more stable than the homogeneous phase at zero temperature. If we include a bare fermion mass, the problem reduces again to solved problems in one-flavor models provided that either the fermionic or the isospin chemical potentials vanish. In the general case, a stability analysis is used to construct the perturbative phase boundary between homogeneous and inhomogeneous phases. This is sufficient to get a good overview of the complete phase diagram. Missing non-perturbative phase boundaries requiring a full numerical Hartree-Fock calculation will be presented in future work.