A fully interacting many-electron-phonon system in one dimension: An exactly soluble model

Abstract

A one-dimensional electron gas problem is investigated within the framework of the Luttinger model incorporating both the electron-acoustic-phonon interaction and the electron-optical-phonon interaction together with the electron-electron interaction. It is shown that this model is exactly soluble and the energy spectrum is constituted by bosonic excitations. It is also shown that for certain values of the coupling parameters the system exhibits an instability indicating the possibility of a phase transition.