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The hierarchical quantum master equation (HQME) approach is an accuratemethod to describe quantum transport in interacting nanosystems. It generalizesperturbative master equation approaches by including higher-order contributionsas well as non-Markovian memory and allows for the systematic convergence tothe numerically exact result. As the HQME method relies on a decomposition ofthe bath correlation function in terms of exponentials, however, itsapplication to systems at low temperatures coupled to baths with complexer bandstructures has been a challenge. In this publication, we outline an extensionof the HQME approach, which uses a re-summation over poles and can be appliedto calculate transient currents at a numerical cost that is independent oftemperature and band structure of the baths. We demonstrate the performance ofthe extended HQME approach for noninteracting tight-binding model systems ofincreasing complexity as well as for the spinless Anderson-Holstein model.

Extending the hierarchical quantum master equation approach to low temperatures and realistic band structures