Pion condensation and QCD phase diagram at finite isospin density

TL;DR

This study uses an effective QCD model to explore pion condensation and chiral phase transitions at finite isospin density, revealing conditions for inhomogeneous condensates and phase boundaries consistent with lattice simulations.

Contribution

It provides a detailed analysis of the phase diagram at finite isospin density using the Polyakov-loop extended quark-meson model, including inhomogeneous chiral condensates and their competition with pion condensates.

Findings

Inhomogeneous chiral condensates exist only for pion masses below 37.1 MeV.

Pion condensation transition is second order for all isospin chemical potentials.

No pion condensation occurs above approximately 187 MeV temperature.

Abstract

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study 1) the possibility of inhomogeneous chiral condensates and its competition with a homogeneous pion condensate in the $\mu$--$\mu_I$ plane at $T=0$ and 2) the phase diagram in the $\mu_I$--$T$ plane. In the $\mu$--$\mu_I$ plane, we find that an inhomogeneous chiral condensate only exists for pion masses lower that 37.1 MeV and does not coexist with a homogeneous pion condensate. In the $\mu_I$--$T$ plane, we find that the phase transition to a Bose-condensed phase is of second order for all values of $\mu_I$ and we find that there is no pion condensation for temperatures larger than approximately 187 MeV. The chiral critical line joins the critical line for pion condensation at a point, whose position depends on the Polyakov-loop potential and the sigma mass. For larger values of $\mu_I$ these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken $O(2)$ symmetry. We compare our results with recent lattice simulations and find overall good agreement