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Charge-density-waves and superconductivity as an alternative to phase separation in the infinite-U Hubbard-Holstein model

We investigate the density instabilities present in the infinite-U Hubbard-Holstein model both at zero and finite momenta as well as the occurrence of Cooper instabilities with a specific emphasis on the role of long-range Coulomb forces. In carrying out this analysis a special attention is devoted to the effects of the strong local $e$-$e$ interaction on the $e$-$ph$ coupling and particularly to both the static and dynamic screening processes dressing this coupling. We also clarify under which conditions in strongly correlated electron systems a weak additional interaction, e.g. a phonon-mediated attraction, can give rise to a charge instability. In the presence of long-range Coulomb forces, the frustrated phase separation leads to the formation of incommensurate charge density waves. These instabilities, in turn, lead to strong residual scattering processes between quasiparticles and to superconductivity, thus providing an interesting clue to the interpretation of the physics of the copper oxides.