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

TL;DR

This paper extends the hierarchical quantum master equation (HQME) method to efficiently handle low temperatures and complex band structures in quantum transport, enabling accurate transient current calculations in nanosystems.

Contribution

We develop an extended HQME approach using pole re-summation, allowing temperature- and band structure-independent calculations of transient currents.

Findings

Effective for noninteracting tight-binding models of increasing complexity

Successfully applied to the spinless Anderson-Holstein model

Maintains systematic convergence to exact results

Abstract

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