Comparative study of many-body perturbation theory and time-dependent density functional theory in the out-of-equilibrium Anderson model

TL;DR

This study compares many-body perturbation theory and time-dependent density functional theory in simulating out-of-equilibrium electron transport in the Anderson model, highlighting their accuracy and limitations against benchmark tDMRG results.

Contribution

It provides a detailed comparison of various theoretical approaches, including Hartree-Fock, second Born, GW, T-Matrix, and TDDFT with ABALDA, for out-of-equilibrium Anderson model transport.

Findings

Second Born approximation closely matches tDMRG results.

TDDFT with ABALDA accurately predicts impurity densities.

TDDFT overestimates currents due to lead density overestimation.

Abstract

We study time-dependent electron transport through an Anderson model. The electronic interactions on the impurity site are included via the self-energy approximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix level as well as within a time-dependent density functional (TDDFT) scheme based on the adiabatic Bethe-Ansatz local density approximation (ABALDA) for the exchange correlation potential. The Anderson model is driven out of equilibrium by applying a bias to the leads and its nonequilibrium dynamics is determined by real-time propagation. The time-dependent currents and densities are compared to benchmark results obtained with the time-dependent density matrix renormalization group (tDMRG) method. Many-body perturbation theory beyond HF gives results in close agreement with tDMRG especially within the 2B approximation. We find that the TDDFT approach with the ABALDA approximation produces accurate results for the densities on the impurity site but overestimates the currents. This problem is found to have its origin in an overestimation of the lead densities which indicates that the exchange correlation potential must attain nonzero values in the leads.