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

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 $\mu_I$--$T$ plane where $\mu_I$ is the isospin chemical potential. In particular, we focus on the Bose condensation of charged pions. At $T=0$, the onset of pion condensation is at $\mu_I={1\over2}m_{\pi}$ in accordance with exact results. The phase transition to a Bose-condensed phase is of second order for all values of $\mu_I$ and in the $O(2)$ universality 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 $\mu_I$ 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.