Inhomogeneous condensation in effective models for QCD using the finite-mode approach

TL;DR

This paper employs the finite-mode numerical approach to study inhomogeneous condensates in effective QCD models, overcoming previous ansatz limitations and accurately reproducing known results while exploring the phase diagram in 3+1 dimensions.

Contribution

It introduces a versatile finite-mode method for analyzing inhomogeneous phases in QCD models, removing previous restrictions on condensate spatial dependence.

Findings

Successfully reproduces known 1+1D model results

Determines the phase diagram of the 3+1D NJL model

Identifies the inhomogeneous phase at high density

Abstract

We use a numerical method, the finite-mode approach, to study inhomogeneous condensation in effective models for QCD in a general framework. Former limitations of considering a specific ansatz for the spatial dependence of the condensate are overcome. Different error sources are analyzed and strategies to minimize or eliminate them are outlined. The analytically known results for $1+1$ dimensional models (such as the Gross-Neveu model and extensions of it) are correctly reproduced using the finite-mode approach. Moreover, the NJL model in $3+1$ dimensions is investigated and its phase diagram is determined with particular focus on the inhomogeneous phase at high density.