Charge instabilities and electron-phonon interaction in the   Hubbard-Holstein model
  We consider the Hubbard-Holstein model in the adiabatic limit to investigate the effects of electron-electron interactions on the electron-phonon coupling. To this aim we compute at any momentum and filling the static charge susceptibility of the Hubbard model within the Gutzwiller approximation and we find that electron-electron correlations effectively screen the electron coupling to the lattice. This screening is more effective at large momenta and, as a consequence, the charge-density wave phase due to the usual Peierls instability of the Fermi surface momenta is replaced by a phase-separation instability when the correlations are sizable. 
A. Di Ciolo, J. Lorenzana, M. Grilli, and G. Seibold