Functional renormalization group approach to transport through correlated quantum dots

We investigate the effect of local Coulomb correlations on electronic transport through a variety of coupled quantum dot systems connected to Fermi liquid leads. We use a newly developed functional renormalization group scheme to compute the gate voltage dependence of the linear conductance, the transmission phase, and the dot occupancies. A detailed derivation of the flow equations for the dot level positions, the inter-dot hybridizations, and the effective interaction is presented. For specific setups and parameter sets we compare the results to existing accurate numerical renormalization group data. This shows that our approach covers the essential physics and is quantitatively correct up to fairly large Coulomb interactions while being much faster, very flexible, and simple to implement. We then demonstrate the power of our method to uncover interesting new physics. In several dots coupled in series the combined effect of correlations and asymmetry leads to a vanishing of transmission resonances. In contrast, for a parallel double-dot we find parameter regimes in which the two-particle interaction generates additional resonances.