A finite-frequency functional RG approach to the single impurity Anderson model

TL;DR

This paper applies a frequency-dependent functional renormalization group method to the single impurity Anderson model, improving the description of finite-energy properties and comparing favorably with numerical renormalization group data at small to intermediate interactions.

Contribution

It introduces a frequency-dependent FRG approach with a simplified parametrization of the two-particle vertex for better finite-energy property analysis.

Findings

FRG with frequency dependence matches NRG data at small to intermediate U.

Frequency-independent FRG captures large U Kondo physics better.

The proposed parametrization reduces computational effort significantly.

Abstract

We use the Matsubara functional renormalization group (FRG) to describe electronic correlations within the single impurity Anderson model. In contrast to standard FRG calculations, we account for the frequency-dependence of the two-particle vertex in order to address finite-energy properties (e.g, spectral functions). By comparing with data obtained from the numerical renormalization group (NRG) framework, the FRG approximation is shown to work well for arbitrary parameters (particularly finite temperatures) provided that the electron-electron interaction U is not too large. We demonstrate that aspects of (large U) Kondo physics which are described well by a simpler frequency-independent truncation scheme are no longer captured by the 'higher-order' frequency-dependent approximation. In contrast, at small to intermediate U the results obtained by the more elaborate scheme agree better with NRG data. We suggest to parametrize the two-particle vertex not by three independent energy variables but by introducing three functions each of a single frequency. This considerably reduces the numerical effort to integrate the FRG flow equations.