Diagrammatic content of the DMFT for the Holstein polaron problem in finite dimensions

Abstract

In the context of the Holstein polaron problem it is shown that the dynamical mean field theory (DMFT) corresponds to the summation of a special class of local diagrams in the skeleton expansion of the self-energy. In the real space representation, these local diagrams are characterized by the absence of vertex corrections involving phonons at different lattice sites. Such corrections vanish in the limit of infinite dimensions, for which the DMFT provides the exact solution of the Holstein polaron problem. However, for finite dimensional systems the accuracy of the DMFT is limited. In particular, it cannot describe correctly the adiabatic spreading of the polaron over multiple lattice sites. Arguments are given that the DMFT limitations on vertex corrections found for the Holstein polaron problem persist for finite electron densities and arbitrary phonon dispersion.

5 pages, 3 figures

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Cited by in corpus (5)

• Momentum average approximation for models with electron-phonon coupling dependent on the phonon momentum
• Phase diagram of the Holstein polaron in one dimension
• Bipolarons and polarons in the Holstein-Hubbard model: Analogies and differences
• Exact solution of electronic transport in semiconductors dominated by scattering on polaronic impurities
• Spectral Functions of the Holstein Polaron: Exact and Approximate Solutions