ELECTRON-PHONON INTERACTION IN ONE-DIMENSION - EXTENDED TOMONAGA-LUTTINGER MODEL

On the basis of the extended Hubbard model we consider phonon mediated forward scattering in one-dimensional systems. Exact results for the two-particle spectral functions are derived for the case when Umklapp and backward scattering due to electron-electron interaction are negle cted. Due to the electron-phonon interaction the phase diagram of the interacting electron system changes remarkably. In dependence on the p honon frequency and on the electron-phonon coupling constant a new div ergence may appear in a two-particle spectral function or an existing one may be removed. The inclusion of Umklapp and backward scattering l eads to the appearance of an energy gap and a polaron energy shift. Th e electron-phonon coupling constant is strongly renormalized and vanis hes faster than the charge velocity as half-filling is approached. Bey ond half-filling the polaron shift may diverge at certain valves of th e coupling parameters. This divergency is related to the Wentzel-Barde en singularity.