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Sum rules and vertex corrections for electron-phonon interactions

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Rösch,  O.
Former Departments, Max Planck Institute for Solid State Research, Max Planck Society;

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Sangiovanni,  G.
Department Quantum Many-Body Theory (Walter Metzner), Max Planck Institute for Solid State Research, Max Planck Society;
Former Departments, Max Planck Institute for Solid State Research, Max Planck Society;

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Gunnarsson,  O.
Former Departments, Max Planck Institute for Solid State Research, Max Planck Society;
Department Nanoscale Science (Klaus Kern), Max Planck Institute for Solid State Research, Max Planck Society;
Department Electronic Structure Theory (Ali Alavi), Max Planck Institute for Solid State Research, Max Planck Society;

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Citation

Rösch, O., Sangiovanni, G., & Gunnarsson, O. (2007). Sum rules and vertex corrections for electron-phonon interactions. Physical Review B, 75(3): 035119.


Cite as: https://hdl.handle.net/21.11116/0000-000E-B50C-9
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 interaction in 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.