Functional-integral approach to an exactly soluble one-dimensional electron-phonon system

We consider forward-scattering electron-electron and electron-phonon interactions in an extended Tomonaga-Luttinger model. The method of functional integration over anticommuting fields gives us a bosonized effective action. This enables us to obtain the spectrum and the correlation functions of the system exactly. We consider couplings to both acoustic and optical phonons. In the case of acoustic phonons, we obtain T→0 phase diagram in the plane of coupling constants which indicates the existence of a normal phase between the regions of charge-density-wave and superconducting instabilities. This is qualitatively different from previous results.