A Quantum Monte Carlo Method and Its Applications to Multi-Orbital Hubbard Models

TL;DR

This paper introduces a quantum Monte Carlo framework for multi-orbital Hubbard models, enabling the study of complex phase transitions without the minus sign problem, demonstrated on a two-band model.

Contribution

A new auxiliary field quantum Monte Carlo method tailored for multi-orbital Hubbard models, allowing exploration of various phase transitions without sign issues.

Findings

Successfully applied to a two-band model

Analyzed ground state properties

Identified potential for studying phase transitions

Abstract

We present a framework of an auxiliary field quantum Monte Carlo (QMC) method for multi-orbital Hubbard models. Our formulation can be applied to a Hamiltonian which includes terms for on-site Coulomb interaction for both intra- and inter-orbitals, intra-site exchange interaction and energy differences between orbitals. Based on our framework, we point out possible ways to investigate various phase transitions such as metal-insulator, magnetic and orbital order-disorder transitions without the minus sign problem. As an application, a two-band model is investigated by the projection QMC method and the ground state properties of this model are presented.