  We investigate theta-vacuum effects on the QCD phase diagram for the
realistic 2+1 flavor system, using the three-flavor Polyakov-extended
Nambu-Jona-Lasinio (PNJL) model and the entanglement PNJL model as an extension
of the PNJL model. The theta-vacuum effects make the chiral transition sharper.
For large theta-vacuum angle the chiral transition becomes first order even if
the quark number chemical potential is zero, when the entanglement coupling
between the chiral condensate and the Polyakov loop is taken into account. We
finally propose a way of circumventing the sign problem on lattice QCD with
finite theta.
