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# Loughborough University Institutional Repository

 Please use this identifier to cite or link to this item: https://dspace.lboro.ac.uk/2134/1144

 Title: Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime Authors: Alexandrov, A.S. Issue Date: 2001 Abstract: In view of some recent works on the role of vertex corrections in the electron-phonon system we readress an important question of the validity of the Migdal-Eliashberg theory. Based on the solution of the Holstein model and inverse coupling constant expansion, we argue that the standard Feynman-Dyson perturbation theory by Migdal and Eliashberg with or without vertex corrections cannot be applied if the electron-phonon coupling constant $\lambda$ is larger than 1 for any ratio of the phonon and Fermi energies. In the extreme adiabatic limit of the Holstein model electrons collapse into self-trapped small polarons or bipolarons due to spontaneous translational-symmetry breaking when $\lambda$ is between 0.5 and 1.3 (depending on the lattice dimensionality). With the increasing phonon frequency the region of the applicability of the theory shrinks to lower values of the coupling constant. Description: This is a pre-print. URI: https://dspace.lboro.ac.uk/2134/1144 Appears in Collections: Pre-Prints (Physics)

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