Chiral spiral in the presence of chiral imbalance

TL;DR

This paper explores the phase structure of the two-dimensional NJL model with chiral imbalance, revealing how a chiral spiral forms and behaves under different conditions, extending previous static analyses to include a chiral chemical potential.

Contribution

It generalizes the understanding of chiral spirals in the NJL model by incorporating chiral chemical potential and clarifying the connection between static and dynamic approaches.

Findings

Chiral spiral radius vanishes at critical temperature.

Period depends only on chemical potential.

Static and dynamic approaches are connected via a half-local symmetry.

Abstract

The phase diagram of the two-dimensional Nambu-Jona-Lasinio (or chiral Gross-Neveu) model is characterized by an order parameter in the form of a chiral spiral. Its radius vanishes at a critical temperature, its period depends only on the chemical potential. We generalize these findings to chirally imbalanced systems by including a chiral chemical potential $\mu_5$. The relationship between the present, static approach and a previous, time dependent one is traced back to a half-local symmetry which the NJL$_2$ model shares with massless Dirac fermions, but which has been neglected so far. The structure of chiral spiral matter is further elucidated by computing fermion and antifermion momentum distribution functions, using a Bogoliubov transformation.