Steady-state properties of multi-orbital systems using quantum Monte Carlo

TL;DR

This paper introduces a numerically exact inchworm quantum Monte Carlo method that effectively mitigates sign problems, enabling accurate simulation of multi-orbital quantum impurity systems in both equilibrium and steady states.

Contribution

The paper presents a novel inchworm Monte Carlo approach that overcomes sign problems in multi-orbital systems, allowing for efficient equilibrium and nonequilibrium steady-state simulations.

Findings

Method successfully alleviates sign problems in multi-orbital models.

Accurate results verified against analytical and previous numerical methods.

Enables simulation of complex quantum impurity systems in steady states.

Abstract

A precise dynamical characterization of quantum impurity models with multiple interacting orbitals is challenging. In quantum Monte Carlo methods, this is embodied by sign problems. A dynamical sign problem makes it exponentially difficult to simulate long times. A multi-orbital sign problem generally results in a prohibitive computational cost for systems with multiple impurity degrees of freedom even in static equilibrium calculations. Here, we present a numerically exact inchworm method that simultaneously alleviates both sign problems, enabling simulation of multi-orbital systems directly in the equilibrium or nonequilibrium steady-state. The method combines ideas from the recently developed steady-state inchworm Monte Carlo framework [Phys. Rev. Lett. 130, 186301 (2023)] with other ideas from the equilibrium multi-orbital inchworm algorithm [Phys. Rev. Lett. 124, 206405 (2020)]. We verify our method by comparison with analytical limits and numerical results from previous methods.