A functional renormalization group approach to zero-dimensional interacting systems

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