Hopping-integral expansion from the limit of zero bandwidth in the infinite-dimensional Hubbard-Holstein model.

We make a careful perturbation analysis of the electronic self-energy Sigma in terms of the effective electron hopping integral A in the infinite-dimensional system. We apply this formal analysis to the system in which the attractive interaction between electrons mediated by local optic phonons competes with the electron-electron short-range repulsion. By summing the most divergent terms in Sigma up to infinite order, we discuss the dynamical localization-delocalization transition.