Renormalization of the electron-phonon coupling in the one-band Hubbard model

We investigate the effect of electronic correlations on the coupling of electrons to Holstein phonons in the one-band Hubbard model. We calculate the static electron-phonon vertex within the linear response of Kotliar-Ruckenstein slave bosons in the paramagnetic saddle-point approximation. Within this approach the on-site Coulomb interaction U strongly suppresses the coupling to Holstein phonons at low temperatures. Moreover, the vertex function does not show particularly strong forward scattering. Going to larger temperatures kTsimilar tot we find that after an initial decrease with U, the electron-phonon coupling starts to increase with U, confirming a recent result of Cerruti, Cappelluti, and Pietronero. We show that this behavior is related to an unusual reentrant behavior from a phase separated to a paramagnetic state upon decreasing the temperature.