  We illustrate the algorithmic advantages of the recently introduced
single-boson exchange (SBE) formulation for the one-loop functional
renormalization group (fRG), by applying it to the two-dimensional Hubbard
model on a square lattice. We present a detailed analysis of the fermion-boson
Yukawa couplings and of the corresponding physical susceptibilities by studying
their evolution with temperature and interaction strength, both at half filling
and finite doping. The comparison with the conventional fermionic fRG
decomposition shows that the rest functions of the SBE algorithm, which
describe correlation effects beyond the SBE processes, play a negligible role
in the weak-coupling regime above the pseudo-critical temperature, in contrast
to the rest functions of the conventional fRG. Remarkably, they remain finite
also at the pseudo-critical transition, whereas the corresponding rest
functions of the conventional fRG implementation diverge. As a result, the SBE
formulation of the fRG flow allows for a substantial reduction of the numerical
effort in the treatment of the two-particle vertex function, paving a promising
route for future multiboson and multiloop extensions.
