  We present a reformulation of the functional renormalization group (fRG) for
many-electron systems, which relies on the recently introduced single boson
exchange (SBE) representation of the parquet equations [Phys. Rev. B 100,
155149 (2019)]. The latter exploits a diagrammatic decomposition, which
classifies the contributions to the full scattering amplitude in terms of their
reducibility with respect to cutting one interaction line, naturally
distinguishing the processes mediated by the exchange of a single boson in the
different channels. We apply this idea to the fRG by splitting the one-loop fRG
flow equations for the vertex function into SBE contributions and a residual
four-point fermionic vertex. Similarly as in the case of parquet solvers,
recasting the fRG algorithm in the SBE representation offers both computational
and interpretative advantages: the SBE decomposition not only significantly
reduces the numerical effort of treating the high-frequency asymptotics of the
flowing vertices, but it also allows for a clear physical identification of the
collective degrees of freedom at play. We illustrate the advantages of an SBE
formulation of fRG-based schemes, by computing through the merger of dynamical
mean-field theory and fRG the susceptibilities and the Yukawa couplings of the
two-dimensional Hubbard model from weak to strong coupling, for which we also
present an intuitive physical explanation of the results. The SBE formulation
of the one-loop flow equations paves a promising route for future multiboson
and multiloop extensions of fRG-based algorithms.
