Finite-temperature Mott transitions in the multiorbital Hubbard model

We investigate the Mott transitions in the multiorbital Hubbard model at half-filling by means of the self-energy functional approach. The phase diagrams are obtained at finite temperatures for the Hubbard model with up to fourfold degenerate bands. We discuss how the first-order Mott transition points $U_{c1}$ and $U_{c2}$ as well as the critical temperature $T_c$ depend on the orbital degeneracy. It is elucidated that enhanced orbital fluctuations play a key role to control the Mott transitions in the multiorbital Hubbard model.

Figure 1

The grand potential $\Omega \left(V\right)$ for the two-orbital model $(M=2)$ as a function of $V$ for different $U$ at $T=0$. Crosses correspond to stationary points.

Figure 2

(Left panel) The grand potential $\Omega$ as a function of the effective hybridization $V$ for $U=7$. Closed circles and triangles represent the stationary points for the metallic and the Mott insulating states. Diamonds denote unstable stationary points. (Right panel) Stationary values of the grand potential as a function of the temperature $T$ for $U=7$. Symbols are the same as in the left panel.

Figure 3

The effective hybridization $V$ as a function of $U$ at $T=0.04$. Inset shows the grand potential as a function of $U$ at $T=0.04$, where ${\Omega }_M\left({\Omega }_I\right)$ is the grand potential for the metallic (insulating) state.

Figure 4

The quasiparticle weight $Z$ as a function of the Coulomb interaction $U$ for the system with $M=1,2,3,4$ at $T=0$. The inset is the enlarged figure in the small $U$ region.

Figure 5

Phase diagrams for the degenerate Hubbard model with the orbital degeneracy $M=1,2,3,4$.

Figure 6

The critical points $U_{c2}(T=0)[=U_c(T=0)]$, $U_c(T=T_c)$, $U_{c1}(T\to 0)$ and the critical temperature $T_c$ as a function of the orbital degeneracy $M$.

Figure 7

Phase diagrams for the two-orbital Hubbard model with the Hund coupling $J=0.1U$ under the condition $U=U^{\prime }+2J$. For clarity, we also show the results at $J=0$.