Inhomogeneous phases in the Nambu-Jona-Lasino and quark-meson model

TL;DR

This paper investigates inhomogeneous ground states in the NJL and quark-meson models, showing how lower-dimensional solutions can inform the 3+1D case and revealing phase diagram modifications with inhomogeneous phases replacing first-order transitions.

Contribution

It extends known lower-dimensional solutions to the 3+1D NJL model and maps out the phase diagram, highlighting the emergence of inhomogeneous phases.

Findings

Inhomogeneous phases replace the first-order transition line in the phase diagram.

Numerical phase diagrams show inhomogeneous regions bordered by second-order lines.

Focus on critical points and zero-temperature behavior.

Abstract

We discuss inhomogeneous ground states of the Nambu-Jona-Lasino (NJL) and quark-meson (QM) model within mean-field approximation and their possible existence in the respective phase diagrams. For this purpose we focus on lower dimensional modulations and point out that known solutions in the 2+1 and 1+1 dimensional (chiral) Gross-Neveu (GN) model can be lifted to the to the 3+1 dimensional NJL model. This is worked out in detail for one-dimensional modulations and numerical results for the phase diagrams are presented. Focus is put on the critical point and on vanishing temperatures. As an interesting result the first order transition line in the phase diagram of homogeneous phases gets replaced by an inhomogeneous phase which is bordered by two second order transition lines.