Phonon Effects on Spin-Charge Separation in One Dimension

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. A signature of electrons pairing in weak interaction regimes was found to be consistent with the existence of a metallic phase proposed recently by Clay and Hardikar [Phys. Rev. Lett. \textbf{95}, 096401 (2005)]. By a comparison between our result and the experimental data of TTF-TCNQ, it is observed that electron-phonon interaction must be taken into account even in the strongly correlated system.