  We extend the Polyakov-loop extended Nambu-Jona-Lasinio (PNJL) model by
introducing an effective four-quark vertex depending on Polyakov loop. The
effective vertex generates entanglement interactions between Polyakov loop and
chiral condensate. The new model is consistent with lattice QCD data at
imaginary quark-number chemical potential and real and imaginary isospin
chemical potentials, particularly on strong correlation between the chiral and
deconfinement transitions and also on the quark-mass dependence of the order of
the Roberge-Weiss endpoint predicted by lattice QCD very lately. We investigate
an influence of the entanglement interactions on a location of the tricritical
point at real isospin chemical potential and a location of the critical
endpoint at real quark-number chemical potential.
