Parametrizations of local vertex corrections from weak to strong coupling: importance of the Hedin three-leg vertex

Harkov, Viktor; Lichtenstein, Alexander I.; Krien, Friedrich

doi:10.48550/arxiv.2104.11534

Cited by 1 publication

(2 citation statements)

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“…[14] (see also Ref. [83]). Both approaches rely on a similar classification of the diagrams contributing to the two-particle reducible contribution to the vertex function.…”

Section: Appendix C: Numerical Implementationmentioning

confidence: 96%

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

Bonetti,

Toschi,

Hille

et al. 2021

Preprint

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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.

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“…[14] (see also Ref. [83]). Both approaches rely on a similar classification of the diagrams contributing to the two-particle reducible contribution to the vertex function.…”

Section: Appendix C: Numerical Implementationmentioning

confidence: 96%

“…In this subsection, we focus on the second main ingredient of the SBE formalism, that is the (fermion-boson) Yukawa couplings, s. also Refs. [47,67,82,83]. The corresponding results for the magnetic and the charge sector are shown in Fig.…”

Section: Yukawa Couplingsmentioning

confidence: 99%