Dynamical mean-field theory of the Hubbard-Holstein model at half-filling: electron-phonon interaction effects on the finite temperature Mott transition

We study the Hubbard-Holstein (HH) model which indludes both the electron-electron and electron-phonon interactins characterized by $U$ and $g$, respectively, by empolying the dynamical mean-field theory in combination with Wilson's numerical renormalization group technique. We fix $g=0.1W$ ($W$=bandwidth of the conduction electrons) and calculate the finite temperature phase diagram of metal-insulator transition in the $U-T$ plane. We will discuss in particular how the critical $U$ values, $U_{c1}$ and $U_{c2}$ , and the critical temperature $T_{c}$ of the Mott transition are changed by the electron-phonon interaction.