  We investigate the chiral condensate and the dressed Polyakov loop or dual
chiral condensate at finite temperature and density in two-flavor
Nambu--Jona-Lasinio model. The dressed Polyakov loop is regarded as an
equivalent order parameter of deconfinement phase transition in a confining
theory. We find the behavior of dressed Polyakov loop in absence of any
confinement mechanism is quite interesting, with only quark degrees of freedom
present, it still shows an order parameter like behavior. It is found that in
the chiral limit, the critical temperature for chiral phase transition
coincides with that of the dressed Polyakov loop in the whole $(T,\mu)$ plane.
In the case of explicit chiral symmetry breaking, it is found that the
transition temperature for chiral restoration $T_c^{\chi}$ is smaller than that
of the dressed Polyakov loop $T_c^{{\cal D}}$ in the low baryon density region
where the transition is a crossover. With the increase of current quark mass
the difference between the two transition temperatures is found to be
increasing. However, the two critical temperatures coincide in the high baryon
density region where the phase transition is of first order. We give an
explanation on the feature of $T_c^{\chi}=T_c^{\cal D}$ in the case of 1st and
2nd order phase transitions, and $T_c^{\chi}<T_c^{\cal D}$ in the case of
crossover, and expect this feature is general and can be extended to full QCD
theory. Our result might indicate that in the case of crossover, there exists a
small region where chiral symmetry is restored but the color degrees of freedom
are still confined.

High Energy Physics - Phenomenology;Nuclear Theory