We present a functional renormalization group (fRG) study of the two
dimensional Hubbard model, performed with an algorithmic implementation
which lifts some of the common approximations made in fRG calculations.
In particular, in our fRG flow; (i) we take explicitly into account the
momentum and the frequency dependence of the vertex functions; (ii) we
include the feedback effect of the self-energy; (iii) we implement the
recently introduced multiloop extension which allows us to sum up
all the diagrams of the parquet approximation with
their exact weight. Due to its iterative structure based on successive
one-loop computations, the loop convergence of the fRG results can be
obtained with an affordable numerical effort. In particular, focusing on
the analysis of the physical response functions, we show that the
results become independent from the chosen cutoff
scheme and from the way the fRG susceptibilities are computed, i.e.,
either through flowing couplings to external fields, or through a
“post-processing” contraction of the interaction vertex at the end of
the flow. The presented substantial refinement of fRG-based computation
schemes paves a promising route towards future quantitative fRG analyses
of more challenging systems and/or parameter regimes.
Self-energy feedback and frequency-dependent interactions in the functional renormalization group flow for the two-dimensional Hubbard model