  To examine the insulating mechanism of 5$d$ transition metal oxide
Sr$_2$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 Sr$_2$IrO$_4$ is a "moderately correlated" AF insulator located in
the intermediate coupling region between a Slater-type and a Mott-type
insulators.
