  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).
