Material-based analysis of spin-orbital Mott insulators

TL;DR

This paper develops a comprehensive framework for analyzing spin-orbital Mott insulators using realistic multiorbital models, mean-field theory, and Monte Carlo simulations, demonstrated on 5d-pyrochlore oxides.

Contribution

It introduces a material-based approach combining perturbation theory, mean-field, and Monte Carlo methods to study spin-orbital states in Mott insulators.

Findings

Revealed spin-orbital ordered states in model systems.

Applicable to various Mott insulators with manageable computational effort.

Demonstrated the method on 5d-pyrochlore oxide.

Abstract

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 is applicable to any Mott insulator with reasonable computational cost. The $5d$-pyrochlore oxide is used here as demonstration.