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

References in corpus (5)

• Electron-phonon interaction in the t-J model
• Electron-phonon interaction and antiferromagnetic correlations
• Apparent electron-phonon interaction in strongly correlated systems
• Renormalization of the electron-phonon coupling in the one-band Hubbard model
• Electron-phonon coupling in the self-consistent Born approximation of the t-J model

Cited by in corpus (3)

• 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