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The one-dimensional (1D) $t$-$J$ Holstein model is studied by exactdiagonalization of finite rings using a variational approximation for thephonon states. Due to renormalization effects induced by the phonons, forintermediate electron-phonon coupling, the phase separation (PS) boundary, andwith it the region of dominating superconducting fluctuations is shiftedsubstantially to smaller values of $J/t$ as compared to the pure $t$-$J$ model.Superconducting correlations are weakened through charge density waveinteractions mediated by the phonons. Possible consequences for the high $T_c$oxides are discussed.Comment: 4 pages, Latex2

physical review letters

Coupling to Optical Phonons in the One-Dimensional<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">t</mml:mi></mml:math>-<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi mathvariant="italic">J</mml:mi></mml:math>Model: Effects on the Superconducting Fluctuations and Phase Separation

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