# Inhomogeneous chiral condensate in the quark-meson model

## TL;DR

This paper investigates inhomogeneous chiral condensates within the two-flavor quark-meson model at finite temperature and chemical potential, providing analytic results and exploring phase diagram sensitivities.

## Contribution

It introduces an analytic calculation of the effective potential for inhomogeneous condensates in the quark-meson model, highlighting the impact of model parameters and vacuum fluctuations.

## Key findings

- Inhomogeneous phase size varies with pion mass.
- Vacuum fluctuations significantly affect phase boundaries.
- Analytic form of the effective potential is derived.

## Abstract

The two-flavor quark-meson model is used as a low-energy effective model for QCD to study inhomogeneous chiral condensates at finite %temperature $T$ baryon chemical potential $\mu_B$. The parameters of the model are determined by matching the meson and quark masses, and the pion decay constant to their physical values using the on-shell and modified minimal subtraction schemes. Using a chiral-density wave ansatz for the inhomogeneity, we calculate the effective potential in the mean-field approximation and the result is completely analytic. The size of the inhomogeneous phase depends sensitively on the pion mass and whether one includes the vacuum fluctuations or not. Finally, we briefly discuss the mean-field phase diagram.