Motivated by recent experiments on Sr2IrO4, we study the ground state properties of a two-dimensional three-band Hubbard model with a strong relativistic spin-orbit coupling. Using the exact diagonalization technique, the dynamical magnetic structure factor M(q, ω) is calculated to examine the low-energy magnetic excitations. We find that the low-energy excitations in M(q, ω) are well described by an effective Heisenberg model composed of a local Kramers doublet of an effective total angular momentum Jeff | - | = 1/2. The antiferromagnetic exchange interaction estimated from M(q, ω) is as large as ∼ 80 meV, which is in good quantitative agreement with experiments. To study a possible long-range ordered state in the thermodynamic limit, we use the variational cluster approximation based on the self-energy functional theory, which is parallelized to accelerate the calculations. We find the ground state where the local Kramers doublet is in-plane antiferromagnetic ally ordered.
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