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We use the Polyakov-loop extended two-flavor quark-meson model as alow-energy effective model for QCD to study the phase diagram in the$\mu_I$--$T$ plane where $\mu_I$ is the isospin chemical potential. Inparticular, we focus on the Bose condensation of charged pions. At $T=0$, theonset of pion condensation is at $\mu_I={1\over2}m_{\pi}$ in accordance withexact results. The phase transition to a Bose-condensed phase is of secondorder for all values of $\mu_I$ and in the $O(2)$ universality class. Thechiral critical line joins the critical line for pion condensation at a pointwhose position depends on the Polyakov-loop potential and the sigma mass. Forlarger values of $\mu_I$ these curves are on top of each other. Thedeconfinement line enters smoothly the phase with the broken $O(2)$ symmetry.We compare our results with recent lattice simulations and find overall goodagreement.

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