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Electron–Phonon Interaction in One Dimension: Extended Tomonaga‐ Luttinger Model
Author(s) -
Kleinert P.,
Bryksin V. V.
Publication year - 1997
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/1521-3951(199702)199:2<435::aid-pssb435>3.0.co;2-1
Subject(s) - condensed matter physics , polaron , physics , phonon , coupling constant , electron , scattering , quantum mechanics , singularity , quantum electrodynamics , mathematics , mathematical analysis
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 neglected. Due to the electron–phonon interaction the phase diagram of the interacting electron system changes remarkably. In dependence on the phonon frequency and on the electron–phonon coupling constant a new divergence may appear in a two‐particle spectral function or an existing one may be removed. The inclusion of Umklapp and backward scattering leads to the appearance of an energy gap and a polaron energy shift. The electron–phonon coupling constant is strongly renormalized and vanishes faster than the charge velocity as half‐filling is approached. Beyond half‐filling the polaron shift may diverge at certain values of the coupling parameters. This divergency is related to the Wentzel‐Bardeen singularity.