Pion condensation and the QCD phase diagram at finite isospin density

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 µ–µI plane at T = 0 and 2) the phase diagram in the µI–T plane. In the µ–µI 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 µI–T plane, we find that the phase transition to a Bose-condensed phase is of second order for all values of µI 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 µI 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