  We investigate the QCD phase diagram of isospin asymmetric matter using the
Polyakov loop extended quark meson (PQM) model with vector interaction. The
critical point temperature is found to decrease in isospin asymmetric matter
and disappear at large isospin chemical potential. We also discuss the QCD
phase transition in the neutron star core. From comparison of the QCD phase
diagram in PQM and corresponding baryon and isospin chemical potentials of
neutron star matter in relativistic mean field models, we show that the order
of the chiral phase transition in the neutron star core could be crossover
because of large isospin chemical potential.
