Dynamics of the Anderson impurity model: benchmarking a non-adiabatic exchange-correlation potential in time-dependent density functional theory

TL;DR

This study benchmarks a non-adiabatic exchange-correlation potential in TDDFT for the Anderson impurity model, showing it accurately captures transient dynamics at certain temperatures and offers a computationally efficient alternative to exact methods.

Contribution

It validates a non-adiabatic functional within TDDFT against exact and perturbative results for the Anderson impurity model, demonstrating its accuracy and efficiency.

Findings

Non-adiabatic functional yields accurate transient dynamics at temperatures comparable to hybridization strength.

TDDFT RC-times agree with second-order perturbation theory at higher temperatures.

The approach offers a low-cost alternative to exact methods for impurity model dynamics.

Abstract

In this comparative study we benchmark a recently developed non-adiabatic exchange-correlation potential within time-dependent density functional theory (TDDFT) (Phys.\ Rev.\ Lett.\ {\bf 120}, 157701 (2018)) by (a) validating the transient dynamics using a numerically exact density matrix renormalization group approach as well as by (b) comparing the $RC$-time, a typical linear response quantity, to upto second order perturbation theory results. As a testbed we use the dynamics of the single impurity Anderson model. These benchmarks show that the non-adiabatic functional yields quantitatively accurate results for the transient dynamics for temperatures of the order of the hybridization strength while the TDDFT $RC$-times quantitatively agree with those from second-order perturbation theory for temperatures which are large compared to the hybridization strength. Both results are particularly intriguing given the relatively low numerical cost of a TDDFT calculation (at least compared to exact approaches).