SPIN GAP IN ONE-DIMENSIONAL ELECTRON-PHONON SYSTEMS

The exponents of spin and charge correlations of one-dimensional elect ron systems are calculated by a renormalization-group method. We study combined effects of electron-phonon interaction and the Umklapp proce ss on renormalization flows. As scattering processes are successively integrated out, these two processes are interfered with each other dep ending on the type of electron-phonon coupling, phonon frequency and f illing. We demonstrate how these factors control a spin gap formation and density-wave/superconductor correlations.