Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

Details Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime Breakdown of the Migdal-Eliashberg theory in the strong-coupling adiabatic regime

2001-02-10

arxiv.org/abs/cond-mat/0102189v1

Physics

Condensed Matter

Superconductivity

4 pages, 1 figure

Scientific paper

10.1209/epl/i2001-00492-x

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.

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