A Projection-based Reduced-order Method for Electron Transport Problems with Long-range Interactions

TL;DR

This paper introduces a projection-based reduced-order method for simulating electron transport with long-range interactions, effectively capturing transient dynamics and Coulomb potentials in large quantum systems.

Contribution

It develops a novel reduced-order framework using Petrov-Galerkin projection and domain decomposition to efficiently model electron transport with long-range Coulomb interactions.

Findings

Accurately reproduces electron density profiles in molecular junctions.

Reduces computational complexity for large-scale quantum transport simulations.

Demonstrates effectiveness on Lithium chain molecular junctions.

Abstract

Long-range interactions play a central role in electron transport. At the same time, they present a challenge for direct computer simulations, since sufficiently large portions of the bath have to be included in the computation to accurately compute the Coulomb potential. This article presents a reduced-order approach, by deriving an open quantum model for the reduced density-matrix. To treat the transient dynamics, the problem is placed in a reduced-order framework. The dynamics, described by the Liouville von Neumann equation, is projected to subspaces using a Petrov-Galerkin projection. In order to recover the global electron density profile as a vehicle to compute the Coulomb potential, we propose a domain decomposition approach, where the computational domain also includes segments of the bath that are selected using logarithmic grids. This approach leads to a multi-component self-energy that enters the effective Hamiltonian. We demonstrate the accuracy of the reduced model using a molecular junction built from a Lithium chains.