Diagrammatic Monte Carlo for Dissipative Quantum Impurity Models

TL;DR

This paper introduces a diagrammatic Monte Carlo method for simulating the real-time dynamics of dissipative quantum impurity models, improving convergence and enabling longer time scale analysis.

Contribution

The authors develop a novel Monte Carlo algorithm based on a single real-time contour for dissipative systems, reducing the sign problem compared to traditional approaches.

Findings

Local Markovian dissipation enhances Monte Carlo convergence.

The method allows simulation of longer time scales in dissipative impurity models.

Application to Anderson impurity model reveals effects of dephasing on charge and spin dynamics.

Abstract

We develop a diagrammatic Monte Carlo method for the real-time dynamics of dissipative quantum impurity models. These are small open quantum systems with interaction and local Markovian dissipation, coupled to a large quantum bath. Our algorithm sample the hybridization expansion formulated on a single real-time contour, rather than on the double Keldysh one, as it naturally arises in the thermofield/vectorized representation of the Lindblad dynamics. We show that local Markovian dissipation generally helps the convergence of the diagrammatic Monte Carlo sampling by reducing the sign problem, thus allowing to reach longer time scales as compared to the conventional unitary case. We apply our method to an Anderson impurity model in presence of local dephasing and discuss its effect on the charge and spin dynamics of the impurity.