Numerical Study for the Ground State of Multi-Orbital Hubbard Models

TL;DR

This paper introduces a generalized auxiliary field quantum Monte Carlo method to study the ground state properties of multi-orbital Hubbard models, revealing insights into Mott insulators, insulator-metal transitions, and orbital effects.

Contribution

A new Monte Carlo technique for multi-orbital systems is developed, enabling detailed analysis of ground state properties without the sign problem in certain cases.

Findings

Quantitative characterization of Mott insulating states.

Identification of universality class for insulator-metal transition.

Crossover behavior driven by orbital level splitting.

Abstract

Ground state properties of multi-orbital Hubbard models are investigated by the auxiliary field quantum Monte Carlo method. A Monte Carlo technique generalized to the multi-orbital systems is introduced and examined in detail. The algorithm contains non-trivial cases where the negative sign problem does not exist. We investigate one-dimensional systems with doubly degenerate orbitals by this new technique. Properties of the Mott insulating state are quantitatively clarified as the strongly correlated insulator, where the charge gap amplitude is much larger than the spin gap. The insulator-metal transitions driven by the chemical potential shows a universality class with the correlation length exponent $\nu=1/2$, which is consistent with the scaling arguments. Increasing level split between two orbitals drives crossover from the Mott insulator with high spin state to the band insulator with low spin state, where the spin gap amplitude increases and becomes closer to the charge gap. Experimental relevance of our results especially to Haldane materials is discussed.