Dynamics Of The Anderson Impurity Model: Benchmarking A Nonadiabatic Exchange-Correlation Potential In Time-Dependent Density-Functional Theory

In this comparative study we benchmark a recently developed nonadiabatic exchange-correlation potential within time-dependent density-functional theory (TDDFT) [Phys. Rev. Len. 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 up to second-order perturbation theory results. As a test bed we use the dynamics of the single-impurity Anderson model. These benchmarks show that the nonadiabatic potential 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.