Efficient steady state solver for the hierarchical equations of motion approach: Formulation and application to charge transport through nanosystems

TL;DR

This paper presents an efficient iterative solver for the steady state hierarchical equations of motion, enabling faster simulation of charge transport in nanoscale quantum systems.

Contribution

It introduces a novel iterative approach with preconditioning for solving HEOM, improving computational efficiency for steady state quantum transport problems.

Findings

Significantly reduces computational effort in solving HEOM.

Successfully applied to simulate charge transport in molecular junctions.

Demonstrates improved performance over existing methods.

Abstract

An iterative approach is introduced, which allows the efficient solution of the hierarchical equations of motion (HEOM) for the steady state of open quantum systems. The approach combines the method of matrix equations with an efficient preconditioning technique to reduce the numerical effort of solving the HEOM. Illustrative applications to simulate nonequilibrium charge transport in single-molecule junctions demonstrate the performance of the method.