Abstract
To examine the insulating mechanism of 5$d$ transition metal oxide ${\text{Sr}}_{2}$${\text{IrO}}_{4}$, we study the ground state properties of a three-orbital Hubbard model with a large relativistic spin-orbit coupling on a square lattice. Using a variational Monte Carlo method, we find that the insulating state appearing in the ground state phase diagram for one hole per site varies from a weakly correlated to a strongly correlated antiferromagnetic (AF) state with increasing Coulomb interactions. This crossover is characterized by the different energy gain mechanisms of the AF insulating state, i.e., from an interaction-energy-driven Slater-type insulator to a band-energy-driven Mott-type insulator with increasing Coulomb interactions. Our calculations reveal that ${\text{Sr}}_{2}$${\text{IrO}}_{4}$ is a ``moderately correlated'' AF insulator located in the intermediate coupling region between a Slater-type and a Mott-type insulator.
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