Considering Hubbard models with infinite U, the leading terms of the electronic self-energy due to an on-site electron-phonon interaction are calculated within a 1/N expansion. In particular, the modifications of the Eliashberg function ${\mathrm{\alpha }}^2$F(ω) due to strong correlations are described and calculated for a simple square lattice as a function of doping. We find that the on-site electron-phonon coupling is in general slightly enhanced in forward scattering but dramatically suppressed for scattering with large momentum transfers by correlations. This implies at least in the single-band case that the electron-phonon coupling is greatly reduced in transport quantities and to a much smaller degree in ${\mathrm{\alpha }}^2$F because of electronic correlations.

• Received 15 November 1993

DOI:https://doi.org/10.1103/PhysRevB.49.4395