Electron-Phonon Interaction in One Dimension: Extended Tomonaga- Luttinger Model

Abstract

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 neglected. Due to the electron-phonon interaction the phase diagram of the interacting electron system changes remarkably. In dependence on the phonon frequency and on the electron-phonon coupling constant a new divergence may appear in a two-particle spectral function or an existing one may be removed. The inclusion of Umklapp and backward scattering leads to the appearance of an energy gap and a polaron energy shift. The electron-phonon coupling constant is strongly renormalized and vanishes faster than the charge velocity as half-filling is approached. Beyond half-filling the polaron shift may diverge at certain values of the coupling parameters. This divergency is related to the Wentzel-Bardeen singularity.