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We study time-dependent electron transport through an Anderson model. Theelectronic interactions on the impurity site are included via the self-energyapproximations at Hartree-Fock (HF), second Born (2B), GW, and T-Matrix levelas well as within a time-dependent density functional (TDDFT) scheme based onthe adiabatic Bethe-Ansatz local density approximation (ABALDA) for theexchange correlation potential. The Anderson model is driven out of equilibriumby applying a bias to the leads and its nonequilibrium dynamics is determinedby real-time propagation. The time-dependent currents and densities arecompared to benchmark results obtained with the time-dependent density matrixrenormalization group (tDMRG) method. Many-body perturbation theory beyond HFgives results in close agreement with tDMRG especially within the 2Bapproximation. We find that the TDDFT approach with the ABALDA approximationproduces accurate results for the densities on the impurity site butoverestimates the currents. This problem is found to have its origin in anoverestimation of the lead densities which indicates that the exchangecorrelation potential must attain nonzero values in the leads.

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