  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.
