Dynamical simulation of spin-orbit insulator and application to bilayer iridate

Spin-orbit insulators emerge in 5d electron systems with strong spin-orbit interaction, which can be described by a Hubbard model in the intermediate coupling regime of intra-atomic Coulomb repulsion (U) comparable to the dominant hopping amplitude (t). A reliable calculation in this regime is theoretically challenging because of the lack of a small parameter. We have developed a new numerical approach that enables large-scale numerical simulations (on finite lattices of more than 10,000 sites) of dynamical correlation functions at finite temperatures in a broad range of U/t values. The simulation of the self-consistent density matrix dynamics is combined with sampling from the Boltzmann distribution. As a relevant application of the newly developed method, we have calculated the dynamical spin structure factor of the bilayer iridate Sr₃Ir₂O₇. Our approach gives an excellent account of the experimental observations. The present method can be applied not only to iridates but also to various systems without any restrictions on the hopping amplitudes, lattice geometry, or electron filling fraction.

[1] G.-W. Chern, K. Barros, Z. Wang, H. Suwa, and C. D. Batista, Phys. Rev. B 97, 035120 (2018)