Quantum Monte Carlo in the steady-state

TL;DR

This paper introduces a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models, enabling efficient analysis of steady-state properties without transient dynamics.

Contribution

The paper presents a novel steady-state Monte Carlo method that directly targets steady-state solutions, reducing computational costs and expanding accessible parameter regimes.

Findings

Benchmarking on quantum dots shows accurate Green's functions in noninteracting and Kondo regimes.

The method reveals qualitative differences in the response of correlated materials to bias voltages.

The approach enables studying nonequilibrium steady states more efficiently than previous methods.

Abstract

We present a numerically exact steady-state inchworm Monte Carlo method for nonequilibrium quantum impurity models. Rather than propagating an initial state to long times, the method is directly formulated in the steady-state. This eliminates any need to traverse the transient dynamics and grants access to a much larger range of parameter regimes at vastly reduced computational costs. We benchmark the method on equilibrium Green's functions of quantum dots in the noninteracting limit and in the unitary limit of the Kondo regime. We then consider correlated materials described with dynamical mean field theory and driven away from equilibrium by a bias voltage. We show that the response of a correlated material to a bias voltage differs qualitatively from the splitting of the Kondo resonance observed in bias-driven quantum dots.