K. Yonemitsu et M. Imada, SPIN-GAP PHASE IN NEARLY HALF-FILLED ONE-DIMENSIONAL CONDUCTORS COUPLED WITH PHONONS, Physical review. B, Condensed matter, 54(4), 1996, pp. 2410-2420
Asymptotic properties of nearly half-filled one-dimensional conductors
coupled with phonons are studied through a renormalization-group meth
od. Due to spin-charge coupling via an electron-phonon interaction, th
e spin correlation varies with filling as well as the charge correlati
on. Depending on the relation between cutoff energy scales of the umkl
app process and of the electron-phonon interaction, various phases app
ear. We find a metallic phase with a spin gap and a dominant charge-de
nsity-wave correlation near half filling between a gapless density-wav
e phase (like in the doped repulsive Hubbard model) and a superconduct
or phase with a spin gap. The spin gap is produced by phonon-assisted
backward scatterings that interfere with the umklapp process construct
ively or destructively depending on the character of electron-phonon c
oupling.