Quantum Monte Carlo for multi-orbital systems at steady-state

The description of nonequilibrium or real time dynamics in quantum impurity models with multiple interacting orbitals is challenging. In Monte Carlo methods based on hybridization expansions, this difficulty takes the form of a dynamical sign problem that exacerbates a multi-orbital sign problem already present in equilibrium calculations on the Matsubara contour. The result is a prohibitive computational cost that scales exponentially with both final simulation time and number of orbitals. We present a numerically exact Inchworm method for multi-orbital systems in the steady-state, where the inchworm expansion simultaneously alleviates both sign problems. The method extends our recently developed steady-state inchworm Monte Carlo framework [1] to multi-orbital systems. We demonstrate the performance of our method by comparison with analytical limits, and showcase its usage by considering the response of multi-orbital quantum dot systems to an external bias voltage in the strongly correlated regime. Our method can also be applied within quantum embedding schemes such as nonequilibrium DMFT.

[1] Erpenbeck et al. – Quantum Monte Carlo in the steady-state – arXiv:2207.07547 (2022)