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Phonon effects on spin-charge separation in one dimension are investigated through the calculation of one-electron spectral functions in terms of the recently developed cluster perturbation theory together with an optimized phonon approach. It is found that the retardation effect due to the finiteness of phonon frequency suppresses the spin-charge separation and eventually makes it invisible in the spectral function. By comparing our results with experimental data of TTF-TCNQ, it is observeddoi:10.1103/physrevlett.96.156402 pmid:16712177 fatcat:snyo6z5bvjf2ddht77shhbtqgu