Finite-volume effects on phase transition in the Polyakov-loop extended Nambu-Jona-Lasinio model with a chiral chemical potential

To investigate finite-volume effects on the chiral symmetry restoration and the deconfinement transition and some impacts of possible global topological background for a quantum chromodynamics (QCD) system with $N_f=2$ (two quark flavors), we apply the Polyakov-loop extended Nambu-Jona-Lasinio model by introducing a chiral chemical potential ${\mu }_5$ artificially. The final numerical results indicate that the introduced chiral chemical potential does not change the critical exponents but shifts the location of critical end point (CEP) significantly; the ratios for the chiral chemical potentials and temperatures at CEP, ${\mu }_c\mathrm{/}{\mu }_{5c}$ and $T_c\mathrm{/}{T}_{5c}$, are significantly affected by the system size $R$. The behavior is that $T_c$ increases slowly with ${\mu }_5$ when $R$ is large and $T_c$ decreases first and then increases with ${\mu }_5$ when $R$ is small. It is also found that for a fixed ${\mu }_5$, there is a $R_{\text{min}}$, where the critical end point vanishes, and the whole phase diagram becomes a crossover when $R<R_{\text{min}}$. Therefore, we suggest that for the heavy-ion collision experiments, which is to study the possible location of CEP, the finite-volume behavior should be taken into account.