Diagrammatic Monte Carlo for dissipative quantum impurity models

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 samples 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 timescales as compared to the conventional unitary case. We apply our method to an Anderson impurity model in the presence of local dephasing and discuss its effect on the charge and spin dynamics of the impurity.