Efficient energy resolved quantum master equation for transport calculations in large strongly correlated systems

TL;DR

This paper presents an efficient energy-resolved quantum master equation method for steady-state transport in large, strongly correlated open quantum systems, enabling calculations beyond six orbitals with high accuracy.

Contribution

The authors develop a systematic approximation scheme for quantum master equations that improves computational efficiency and accuracy in transport calculations for large many-body systems.

Findings

Benchmarking on a six-orbital system shows accurate results with destructive interference.

The method scales to systems with Hilbert space sizes around 10^6.

The approach surpasses traditional secular approximations in resolving coherences.

Abstract

We introduce a systematic approximation for an efficient evaluation of Born--Markov master equations for steady state transport studies in open quantum systems out of equilibrium: the energy resolved master equation approach. The master equation is formulated in the eigenbasis of the open quantum system and build successively by including eigenstates with increasing grandcanonical energies. In order to quantify convergence of the approximate scheme we introduce quality factors to check preservation of trace, positivity and hermiticity. Furthermore, we discuss different types of master equations that go beyond the commonly used secular approximation in order to resolve coherences between quasi--degenerate states. For the discussion of complete positivity we introduce a canonical Redfield-Bloch master equation and compare it to a previously derived master equations in Lindblad form with and without using the secular approximation. The approximate scheme is benchmarked for a six orbital quantum system which shows destructive quantum interference under the application of a bias voltage. The energy resolved master equation approach presented here makes quantum transport calculations in many--body quantum systems numerically accessible also beyond six orbitals with a full Hilbert space of the order of $\sim 10^6$.