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In this work we present a comprehensive analysis of collective electronicfluctuations and their effect on single-particle properties of the Hubbardmodel. Our approach is based on a standard dual fermion/boson scheme with theinteraction truncated at the two-particle level. Within this framework wecompare various approximations that differ in the set of diagrams (ladder vsexact diagrammatic Monte Carlo), and/or in the form of the four-pointinteraction vertex (exact vs partially bosonized). This allows to evaluate theeffect of all components of the four-point vertex function on the electronicself-energy. In particular, we observe that contributions that are notaccounted for by the partially bosonized approximation for the vertex have onlya minor effect on electronic degrees of freedom in a broad range of modelparameters. In addition, we find that in the regime, where the ladder dualfermion approximation provides an accurate solution of the problem, the leadingcontribution to the self-energy is given by the longitudional bosonic modes.This can be explained by the fact that contributions of transverseparticle-hole and particle-particle modes partially cancel each other. Ourresults justify the applicability of the recently introduced dual triplyirreducible local expansion (D-TRILEX) method that represents one of thesimplest consistent diagrammatic extensions of the dynamical mean-field theory.We find that the self-consistent D-TRILEX approach is reasonably accurate alsoin challenging regimes of the Hubbard model, even where the dynamicalmean-field theory does not provide the optimal local reference point (impurityproblem) for the diagrammatic expansion.

Impact of partially bosonized collective fluctuations on electronic degrees of freedom