Quark anomalous magnetic moment leads to the inverse magnetic catalysis phenomena of chiral restoration and deconfinement phase transitions in $\mu_B-T$ plane

The effect of quark anomalous magnetic moment (AMM) to chiral restoration and deconfinement phase transitions in baryon chemical potential-temperature $(\mu_B-T)$ plane under magnetic fields is investigated in frame of a Pauli-Villars regularized PNJL model. It's found that the quark AMM plays the role of inverse catalysis to the phase transitions, and large quark AMM will change the magnetic catalysis phenomena of phase transitions to inverse magnetic catalysis in the whole $\mu_B-T$ plane. For a fixed magnetic field, the critical temperature $T_c$ and critical baryon chemical potential $\mu_B^c$ decreases with quark AMM. The stronger the magnetic field is, the inverse catalysis effect of AMM becomes more important. For a small AMM $\kappa=\kappa_1$, it shows the magnetic catalysis effect for critical temperature $T_c$ at vanishing $\mu_B$ with increasing magnetic field, and (inverse) magnetic catalysis effect for critical baryon chemical potential $\mu_B^c$ at vanishing $T$ under (weak) strong magnetic field. At finite $T$ and $\mu_B$, there exist some crossings of the phase transition lines with different magnetic field. For a large AMM $\kappa=\kappa_2$, we obtain the inverse magnetic catalysis effect in the whole $\mu_B-T$ plane, and no crossings of phase transition lines happen.