Chiral density wave versus pion condensation in the 1+1 dimensional NJL model

TL;DR

This paper investigates the phase structure of the 1+1 dimensional NJL model, revealing inhomogeneous chiral-density waves and pion condensates at finite temperature and chemical potentials, with detailed phase diagrams and critical point analysis.

Contribution

It provides a comprehensive analysis of inhomogeneous phases and phase transitions in the NJL model using dimensional regularization and Ginzburg-Landau theory.

Findings

Inhomogeneous chiral-density wave phase exists for all $>_c$ at zero temperature.

Critical and Lifshitz points coincide in the chiral limit.

Rich phase structure with competition between chiral-density wave and pion condensate.

Abstract

In this paper, we study the possibility of an inhomogeneous quark condensate in the 1+1 dimensional Nambu-Jona-Lasinio model in the large-$N_c$ limit at finite temperature $T$ and quark chemical potential $\mu$ using dimensional regularization. The phase diagram in the $\mu$--$T$ plane is mapped out. At zero temperature, an inhomogeneous phase with a chiral-density wave exists for all values of $\mu>\mu_c$. Performing a Ginzburg-Landau analysis, we show that in the chiral limit, the critical point and the Lifschitz point coincide. We also consider the competition between a chiral-density wave and a constant pion condensate at finite isospin chemical potential $\mu_I$. The phase diagram in the $\mu_I$--$\mu$ plane is mapped out and shows a rich phase structure.