P. Kleinert et Vv. Bryksin, ELECTRON-PHONON INTERACTION IN ONE-DIMENSION - EXTENDED TOMONAGA-LUTTINGER MODEL, Physica status solidi. b, Basic research, 199(2), 1997, pp. 435-453
On the basis of the extended Hubbard model we consider phonon mediated
forward scattering in one-dimensional systems. Exact results for the
two-particle spectral functions are derived for the case when Umklapp
and backward scattering due to electron-electron interaction are negle
cted. Due to the electron-phonon interaction the phase diagram of the
interacting electron system changes remarkably. In dependence on the p
honon frequency and on the electron-phonon coupling constant a new div
ergence may appear in a two-particle spectral function or an existing
one may be removed. The inclusion of Umklapp and backward scattering l
eads to the appearance of an energy gap and a polaron energy shift. Th
e electron-phonon coupling constant is strongly renormalized and vanis
hes faster than the charge velocity as half-filling is approached. Bey
ond half-filling the polaron shift may diverge at certain valves of th
e coupling parameters. This divergency is related to the Wentzel-Barde
en singularity.