  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 observed that the electron-phonon
interaction must be taken into account when interpreting the ARPES data.
