Charge fluctuations and electron-phonon interaction in the finite-U Hubbard model

Recent experiments have triggered a renewed interest for a theoretical understanding of the electron–phonon (el–ph) properties in strongly correlated systems. We employ a gaussian expansion within the finite-UU slave-bosons formalism to investigate the momentum structure of the el–ph vertex function in the Hubbard model as function of UU and nn. The suppression of large momentum scattering and the onset of a small-qq peak structure, parametrized by a cut-off qcqc, are shown to be essentially ruled by the band narrowing factor ZMFZMF due to the electronic correlation. A phase diagram of ZMFZMF and qcqc in the whole UU-nn space is presented. Our results are in more than qualitative agreement with a recent numerical analysis and permits the understanding of some anomalous features of the quantum Monte Carlo data.