DMRG study of superconductivity of Hubbard model with electron-phonon interactions

Recently several experimental and theoretical studies suggest that electron-phonon coupling (EPC) could be an essential ingredient in understanding high temperature superconductors. In this work, we investigate the effect of EFC on the Hubbard model by using large-scale density matrix renormalization group. For the $U=8$ Hubbard model with EPC constant $\lambda$ ~ 0.3, we find significant suppression of charge density wave. The influence of phonon on superconductivity and the effect of retardation will also be discussed.