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Metal-insulator transition in three-band Hubbard model with strong spin-orbit interaction

Recent investigations suggest that both spin-orbit coupling and electron correlation play very crucial roles in the $5d$ transition metal oxides. By using the generalized Gutzwiller variational method and dynamical mean-field theory with the hybridization expansion continuous time quantum Monte Carlo as impurity solver, the three-band Hubbard model with full Hund's rule coupling and spin-orbit interaction terms, which contains the essential physics of partially filled $t_{2g}$ sub-shell of $5d$ materials, is studied systematically. The calculated phase diagram of this model exhibits three distinct phase regions, including metal, band insulator and Mott insulator respectively. We find that the spin-orbit coupling term intends to greatly enhance the tendency of the Mott insulator phase. Furthermore, the influence of the electron-electron interaction on the effective strength of spin-orbit coupling in the metallic phase is studied in detail. We conclude that the electron correlation effect on the effective spin-orbit coupling is far beyond the mean-field treatment even in the intermediate coupling region.