A finite-frequency functional renormalization group approach to the single impurityAnderson model

Abstract

We use the Matsubara functional renormalization group (FRG) to describe electroniccorrelations within the single impurity Anderson model. In contrast to standardFRG calculations, we account for the frequency dependence of the two-particlevertex in order to address finite-energy properties (e.g, spectral functions). Bycomparing 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 interactionU is not too large. We demonstrate that aspects of (largeU) Kondo physics which are described well by a simpler frequency-independenttruncation scheme are no longer captured by the ‘higher-order’frequency-dependent approximation. In contrast, at small to intermediateU the results obtained by the more elaborate scheme agree better with NRG data. We suggestto parametrize the two-particle vertex not by three independent energy variables but byintroducing three functions each of a single frequency. This considerably reduces thenumerical effort to integrate the FRG flow equations.