Coupling to Optical Phonons in the One-Dimensionalt-JModel: Effects on the Superconducting Fluctuations and Phase Separation

The one-dimensional $t-J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Because of renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation boundary, and with it the region of dominating superconducting fluctuations is shifted substantially to smaller values of $J/t$ as compared to the pure $t-J$ model. Superconducting correlations are weakened through charge density wave interactions mediated by the phonons. Possible consequences for the high- $T_c$ oxides are discussed.