The two-flavor Polyakov-loop extended model is generalized by taking into account the effective four-quark vector-type interaction with the coupling strengths, which are endowed with a dependence on the Polyakov field Phi. The effective vertex generates entanglement interaction between the Polyakov loop and the chiral condensate. We investigate the influence of an additional quark vector interaction and the entanglement interaction on thermodynamics of a quark system and in particular on the location of the critical end-point at the given chemical potential or quark density. It is shown that the finite value of the singlet vector interaction strength G(v) improves the model agreement with the lattice data. The influence of the nonzero G(v) and entanglement on the thermodynamic observables and the curvature of the crossover boundary in the T - mu plane is also examined.
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