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-U slave-bosons formalism to investigate the momentum structure of the el-ph vertex function in the Hubbard model as function of U and n: The suppression of large momentum scattering and the onset of a small-q peak structure, parametrized by a cut-off qc; are shown to be essentially ruled by the band narrowing factor ZMF due to the electronic correlation. A phase diagram of ZMF and qc in the whole U-n 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.