Phase diagrams of the two-orbital Hubbard model with different bandwidths

We investigate the two-orbital Hubbard model in infinite dimensions by means of the self-energy functional method. By calculating the entropy, susceptibility, and quasi particle weight at zero temperature, we determine the phase diagram for the system with same and different bandwidths, which is compared with that obtained recently. It is clarified that orbital fluctuations play a key role in controlling the nature of the Mott transitions in the system.

Figure 1

The grand potential as a function of the variational parameter $V$. Thick lines correspond to the critical value $U_c$.

Figure 2

The entropy per site as a function of $U$.

Figure 3

The zero-temperature phase diagram for the degenerate Hubbard model with same bandwidths $R=1$. $U_c^I$ $\left(U_c^M\right)$ is the critical point where the insulating (metallic) state disappears. $U_c$ represents the first-order transition points and the shaded region represents the coexisting state.

Figure 4

The local orbital susceptibility in the system with same bandwidths. The inset shows orbital and charge susceptibilities in the case $J=0.03U$.

Figure 5

The quasiparticle weight $Z$ as a function of $U$ obtained from the reference systems $N_b=1$ and $N_b=3$ when $J∕U=0$.

Figure 6

The quasiparticle weight $Z$ as a function of $U$ in the cases $J∕U=0.01$ and $J∕U=0.25$.

Figure 7

The quasiparticle weights for the $\alpha$th orbital $Z_{\alpha }$ when $R=1$ and $0.2$.

Figure 8

The inverse of orbital and spin local susceptibilities as a function of $U$ when $J∕U=0$. The inset shows orbital and charge susceptibilities and the entropy per site when $R=0.17$.

Figure 9

The phase diagram for the case $J∕U=0$. $U_c^I$ $\left(U_c^M\right)$ is the critical point where the insulating (metallic) state becomes unstable with increasing (decreasing) $U$. The dotted lines denote the phase boundaries obtained by a simple estimation (see text).

Figure 10

The local susceptibilities and the entropy per site in the system with different bandwidths $R=0.5$.

Figure 11

The phase diagram when $J∕U=0.01$ and $J∕U=0.1$. The gray region denotes the coexisting state.

Figure 12

The phase diagram for the degenerate Hubbard model with different bandwidths $R=0.1$, 0.5 and 0.8. The black and gray regions denote the OSMI phase and the coexisting state, respectively.