Comparison between scattering-states numerical renormalization group and the Kadanoff-Baym-Keldysh approach to quantum transport: Crossover from weak to strong correlations

The quantum transport through nanoscale junctions is governed by the charging energy $U$ of the device. We employ the recently developed scattering-states numerical renormalization group approach to open quantum systems to study nonequilibrium Green functions and current-voltage characteristics of such junctions for small and intermediate values of $U$. The reliability of the approach is established by the excellent agreement with diagrammatic Kadanoff-Baym-Keldysh results at small values of the $U$. We demonstrate the limits of the diagrammatic approaches at intermediate Coulomb repulsion. These approaches predict two different low-energy scale for magnetic and charge fluctuations in zero bias while the numerical renormalization group approach correctly yields only one single, universal scale. At large voltages and intermediate values of the Coulomb repulsion the self-consistent second Born as well as the GW approximation reproduce the SNRG spectral functions quite well for a symmetric junctions, while for the asymmetric model the voltage-dependent redistribution of spectral weight differs significantly. The second-order perturbation theory does not capture the correct single-particle dynamics at large bias and violates current conservation for asymmetric junctions.