Gunnarsson O., Meden V., Schoenhammer K.
The electron spectral function is calcd. for a model including electron-phonon coupling to Einstein phonons, to study corrections to Migdal's theorem. A cumulant expansion is used for the time-dependent Green's function, and the 2nd and 4th order cumulants are studied. For a 1-band model it is illustrated that Migdal's theorem is valid in the large band width limit for a fixed coupling const. In this limit, the spectrum has at most 1 satellite in addn. to the main peak. As the band width is reduced, the spectrum calcd. with the 4th order cumulant develops multiple satellites, if .epsilon.k is close to the Fermi energy. Although the interband electron-phonon coupling is substantial, and the effective band width may therefore be argued to be large, Migdal's theorem is nevertheless not valid for C60.
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