Functional renormalization group approach to zero-dimensional interacting systems

TL;DR

This paper applies the functional renormalization group method to zero-dimensional quantum systems, demonstrating accurate results for energies and spectra of models like the anharmonic oscillator and Anderson impurity, especially at moderate couplings.

Contribution

It introduces a truncated flow equation approach within the functional renormalization group framework for zero-dimensional systems, providing results comparable to exact and numerical methods.

Findings

FRG results agree well with exact solutions at large couplings

Spectra of the Anderson model are accurately captured at small to intermediate couplings

Low-energy scales like the Kondo temperature are correctly reproduced

Abstract

We apply the functional renormalization group method to the calculation of dynamical properties of zero-dimensional interacting quantum systems. As case studies we discuss 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, 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 then are compared to the results of perturbation theory and the numerical renormalization group. 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 particulare the low-energy scale (Kondo temperature) extracted from the functional renormalization group results shows the expected behavior.