  We apply a functional implementation of the field-theoretical renormalization
group (RG) method up to two loops to the single-impurity Anderson model. To
achieve this, we follow a RG strategy similar to that proposed by Vojta
\emph{et al.} [Phys. Rev. Lett. \textbf{85}, 4940 (2000)], which consists of
defining a soft ultraviolet regulator in the space of Matsubara frequencies for
the renormalized Green's function. Then we proceed to derive analytically and
solve numerically integro-differential flow equations for the effective
couplings and the quasiparticle weight of the present model, which fully treat
the interplay of particle-particle and particle-hole parquet diagrams and the
effect of the two-loop self-energy feedback into them. We show that our results
correctly reproduce accurate numerical renormalization group data for weak to
slightly moderate interactions. These results are in excellent agreement with
other functional Wilsonian RG works available in the literature. Since the
field-theoretical RG method turns out to be easier to implement at higher loops
than the Wilsonian approach, higher-order calculations within the present
approach could improve further the results for this model at stronger
couplings. We argue that the present RG scheme could thus offer a possible
alternative to other functional RG methods to describe electronic correlations
within this model.
