Sum rules and vertex corrections for electron-phonon interactions

Rösch, O.; Sangiovanni, G.; Gunnarsson, O.

Sum rules and vertex corrections for electron-phonon interactions

Authors

Rösch, O.

Sangiovanni, G.

Gunnarsson, O.

Description

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