A Cartesian Quasi-classical Model to Nonequilibrium Quantum Transport: The Anderson Impurity Model

TL;DR

This paper extends a Cartesian quasi-classical approach to model nonequilibrium quantum transport in the Anderson impurity model, accurately capturing phenomena like Coulomb blockade with improved mapping techniques.

Contribution

It introduces a Cartesian quasi-classical method for correlated quantum transport, improving accuracy over previous mappings and capturing key effects like Coulomb blockade.

Findings

Accurate results for the resonant level model across various conditions.

Semi-quantitative agreement for the Anderson impurity model with electron-electron interactions.

Qualitative capture of Coulomb blockade effects.

Abstract

We apply the recently proposed quasi-classical approach for a second quantized many-electron Hamiltonian in Cartesian coordinates [J. Chem. Phys. 137, 154107 (2012)] to correlated nonequilibrium quantum transport. The approach provides accurate results for the resonant level model for a wide range of temperatures, bias and gate voltages, correcting for the flaws of our recently proposed mapping using action-angle variables. When electron-electron interactions are included, higher order schemes are required to map the two-electron integrals, leading to semi-quantitative results for the Anderson impurity model. In particular, we show that the current mapping is capable of capturing qualitatively the Coulomb blockade effect.