Quantum Monte Carlo Method in the Steady State

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.

Automated summary

We propose a numerically exact method for nonequilibrium quantum impurity models, which directly formulates in the steady state, eliminating the need to traverse the transient dynamics and reducing computational costs. The method is benchmarked on quantum dots in the noninteracting and Kondo regime, as well as correlated materials driven away from equilibrium. Qualitative differences are observed in the response to bias voltage between correlated materials and bias-driven quantum dots.