Bosonization of coupled electron-phonon systems
Abstract
We calculate the single-particle Green's function of electrons that are coupled to acoustic phonons by means of higher dimensional bosonization. This non-perturbative method is {\it{not}} based on the assumption that the electronic system is a Fermi liquid. For isotropic three-dimensional phonons we find that the long-range part of the Coulomb interaction cannot destabilize the Fermi liquid state, although for strong electron-phonon coupling the quasi-particle residue is small. We also show that Luttinger liquid behavior in three dimensions can be due to quasi-one-dimensional anisotropy in the electronic band structure {\it{or in the phonon frequencies}}.
Cite
@article{arxiv.cond-mat/9508021,
title = {Bosonization of coupled electron-phonon systems},
author = {Peter Kopietz},
journal= {arXiv preprint arXiv:cond-mat/9508021},
year = {2009}
}
Comments
I have added a few lines to show how the Bohm-Staver relation can be derived within my approach. To appear in Z. Phys. B