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Numerically Exact Long Time Behavior of Nonequilibrium Quantum Impurity Models

A Monte Carlo sampling of diagrammatic corrections to the non-crossing approximation is shown to provide numerically exact estimates of the long-time dynamics and steady state properties of nonequilibrium quantum impurity models. This `bold' expansion converges uniformly in time and significantly ameliorates the sign problem that has heretofore limited the power of real-time Monte Carlo approaches to strongly interacting real-time quantum problems. The new approach enables the study of previously intractable problems ranging from generic long time nonequilibrium transport characteristics in systems with large onsite repulsion to the direct description of spectral functions on the real frequency axis in Dynamical Mean Field Theory.