  Asymptotic properties of nearly-half-filled one-dimensional conductors
coupled with phonons are studied through a renormalization group method. Due to
spin-charge coupling via electron-phonon interaction, the spin correlation
varies with filling as well as the charge correlation. Depending on the
relation between cut-off energy scales of the Umklapp process and of the
electron-phonon interaction, various phases appear. We found a metallic phase
with a spin gap and a dominant charge- density-wave correlation near half
filling between a gapless density-wave phase (like in the doped repulsive
Hubbard model) and a superconductor phase with a spin gap. The spin gap is
produced by phonon-assisted backward scatterings which are interfered with the
Umklapp process constructively or destructively depending on the character of
electron-phonon coupling.
