Spin-gap phase in nearly-half-filled one-dimensional conductors coupled   with phonons
  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. 
K. Yonemitsu (IMS) and M. Imada (ISSP, Univ. of Tokyo)