Relevance of phonon dynamics in strongly correlated systems coupled to phonons: Dynamical mean-field theory analysis

CNR-INFM Statistical Mechanics and Complexity Center, and Dipartimento di FisicaUniversit`a di Roma ”La Sapienza” piazzale Aldo Moro 5, I-00185 Roma, Italy(Dated: February 2, 2008)The properties of the electron-phonon interaction in the presence of a sizable electronic repulsionat finite doping are studied by investigating the metallic phase of the Hubbard-Holstein modelwith Dynamical Mean Field Theory. Analyzing the quasiparticle weight at finite doping, we findthat a large Coulomb repulsion reduces the effect of electron-phonon coupling at low-energy, whilethis reduction is not present at high energy. The renormalization of the electron-phonon couplinginduced by the Hubbard repulsion depends in a surprisingly strong and non-trivial way on thephonon frequency. Our results suggest that phonon might affect differently high-energy and low-energy properties and this, together with the effect of phonon dynamics, should be carefully takeninto account when the effects of the electron-phonon interaction in a strongly correlated system, likethe superconducting cuprates, are discussed.