A functional renormalization group approach to zero-dimensional interactingsystems

Abstract

We apply the functional renormalization group method to the calculation of dynamicalproperties of zero-dimensional interacting quantum systems. We discuss as case studiesthe anharmonic oscillator and the single-impurity Anderson model. We truncatethe hierarchy of flow equations such that the results are at least correct up tosecond-order perturbation theory in the coupling. For the anharmonic oscillator,energies and spectra obtained within two different functional renormalization groupschemes are compared to numerically exact results, perturbation theory results,and the mean field approximation. Even at large coupling, the results obtainedusing the functional renormalization group agree quite well with the numericalexact solution. The better of the two schemes is used to calculate spectra of thesingle-impurity Anderson model, which are then compared to the results fromperturbation theory and the numerical renormalization group ones. For small tointermediate couplings the functional renormalization group gives results which areclose to the ones obtained using the very accurate numerical renormalizationgroup method. In particular, the low energy scale (Kondo temperature) extractedfrom the functional renormalization group results shows the expected behaviour.