Electron-phonon interaction and antiferromagnetic correlations

We study effects of the Coulomb repulsion on the electron-phonon interaction (EPI) in the Holstein-Hubbard model, using the antiferromagnetic (AF) dynamical mean-field approximation. AF correlations strongly enhance EPI effects on the electron Green's function with respect to the paramagnetic correlated system, but the net effect of the Coulomb interaction is a moderate suppression of the EPI. Doping leads to additional suppression. In contrast, the Coulomb interaction strongly suppresses EPI effects on phonons, but the suppression weakens with doping.