Spectral function of the Anderson impurity model at finite temperatures

TL;DR

This paper compares the spectral function calculations of the Anderson impurity model at finite temperatures using FRG and NRG methods, showing good agreement except for zero-temperature Kondo resonance narrowing.

Contribution

It introduces a non-perturbative FRG approach with a Hubbard-Stratonovich field for spin fluctuations and compares it to highly accurate NRG results.

Findings

FRG provides a good spectral line-shape description at finite temperatures.

FRG matches NRG results in weak and strong coupling regimes.

FRG does not reproduce zero-temperature exponential Kondo narrowing.

Abstract

Using the functional renormalization group (FRG) and the numerical renormalization group (NRG), we calculate the spectral function of the Anderson impurity model at zero and finite temperatures. In our FRG scheme spin fluctuations are treated non-perturbatively via a suitable Hubbard-Stratonovich field, but vertex corrections are neglected. A comparison with our highly accurate NRG results shows that this FRG scheme gives a quantitatively good description of the spectral line-shape at zero and finite temperatures both in the weak and strong coupling regimes, although at zero temperature the FRG is not able to reproduce the known exponential narrowing of the Kondo resonance at strong coupling.