Coupling to optical phonons in the one-dimensional t-J model: Effects on superconducting fluctuations and phase separation

The one-dimensional (1D) $t$-$J$ Holstein model is studied by exact diagonalization of finite rings using a variational approximation for the phonon states. Due to renormalization effects induced by the phonons, for intermediate electron-phonon coupling, the phase separation (PS) 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.