Material-based analysis of spin-orbital Mott insulators

We present a framework for analyzing Mott insulators using a material-based tight-binding model. We start with a realistic multiorbital Hubbard model and derive an effective model for the localized electrons through the second-order perturbation theory with respect to intersite hopping. This effective model, known as the Kugel-Khomskii model, is described by SU(N) generators, where N is the number of localized states. We solve this model by the mean-field theory that takes local correlations into account and reveal spin-orbital ordered states. To include spatial correlations, we apply the classical Monte Carlo based on the path-integral approach with SU(N) coherent states, and also derive the equation of motion for spin-orbital degrees of freedom. Our approach enables quantitative analysis of Mott insulator materials with a small intersite quantum correlation. The 5d-pyrochlore oxide is used here as a demonstration.