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We present a reformulation of the functional renormalization group (fRG) formany-electron systems, which relies on the recently introduced single bosonexchange (SBE) representation of the parquet equations [Phys. Rev. B 100,155149 (2019)]. The latter exploits a diagrammatic decomposition, whichclassifies the contributions to the full scattering amplitude in terms of theirreducibility with respect to cutting one interaction line, naturallydistinguishing the processes mediated by the exchange of a single boson in thedifferent channels. We apply this idea to the fRG by splitting the one-loop fRGflow equations for the vertex function into SBE contributions and a residualfour-point fermionic vertex. Similarly as in the case of parquet solvers,recasting the fRG algorithm in the SBE representation offers both computationaland interpretative advantages: the SBE decomposition not only significantlyreduces the numerical effort of treating the high-frequency asymptotics of theflowing vertices, but it also allows for a clear physical identification of thecollective degrees of freedom at play. We illustrate the advantages of an SBEformulation of fRG-based schemes, by computing through the merger of dynamicalmean-field theory and fRG the susceptibilities and the Yukawa couplings of thetwo-dimensional Hubbard model from weak to strong coupling, for which we alsopresent an intuitive physical explanation of the results. The SBE formulationof the one-loop flow equations paves a promising route for future multibosonand multiloop extensions of fRG-based algorithms.

Single boson exchange representation of the functional renormalization group for strongly interacting many-electron systems