Sum rules and vertex corrections for electron-phonon interactions

Abstract

We derive sum rules for the phonon self-energy and the electron-phonon contribution to the electron self-energy of the Holstein-Hubbard model in the limit of large Coulomb interaction U. Their relevance for finite U is investigated using exact diagonalization and dynamical mean-field theory. Based on these sum rules, we study the importance of vertex corrections to the electron-phonon interactionin a diagrammatic approach. We show that they are crucial for a sum rule for the electron self-energy in the undoped system while a sum rule related to the phonon self-energy of doped systems is satisfied even if vertex corrections are neglected. We provide explicit results for the vertex function of a two-site model.

9 pages, 6 figures

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Cited by in corpus (7)

• Interplay between electron-phonon and Coulomb interactions in cuprates
• Aspects of Electron-Phonon Self-Energy Revealed from Angle-Resolved Photoemission Spectroscopy
• Nonequilibrium sum rules for the retarded self-energy of strongly correlated electrons
• Effective enhancement of the electron-phonon coupling driven by nonperturbative electronic density fluctuations
• Intertwined fluctuations and isotope effects in the Hubbard-Holstein model on the square lattice from functional renormalization
• Nonequilibrium sum rules for the Holstein model
• Nonequilibrium spectral moment sum rules of the Holstein-Hubbard model