Nontopological Soliton in the Polyakov Quark Meson Model

Within a mean field approximation, we study a nontopological soliton solution of the Polyakov quark-meson model in the presence of a fermionic vacuum term with two flavors at finite temperature and density. The profile of the effective potential exhibits a stable soliton solution below a critical temperature $T\leq T_{\chi}^c$ for both the crossover and the first-order phase transitions, and these solutions are calculated here with appropriate boundary conditions. However, it is found that only if $T\leq T^c_d$,the energy of the soliton $M_N$ is less than the energy of the three free constituent quarks $3M_q$. As $T> T^c_d$, there is an instant delocalization phase transition from hadron matter to quark matter. The phase diagram together with the location of a critical end point (CEP) has been obtained in $T$ and $\mu$ plane. We notice that two critical temperatures always satisfy $T^c_d\leq T_{\chi}^c$. Finally, we present and compare the result of thermodynamic pressure at zero chemical potential with lattice data.