Pion condensation and phase diagram in the Polyakov-loop quark-meson model

Abstract

We use the Polyakov-loop extended two-flavor quark-meson model as a low-energy effective model for QCD to study the phase diagram in the μI–T planewhere μI is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At T ¼ 0, the onset of pion condensation is at μI ¼ 1 2mπ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of μI and in the Oð2Þuniversality class. 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 μI these curves are on top of each other. The deconfinement line enters smoothly the phase with the broken Oð2Þ symmetry. We compare our results with recent lattice simulations and find overall good agreement.