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 not based on the assumption that the electronic system is a Fermi liquid. For isotropic threedimensional 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 or in the phonon frequencies.
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Kopietz, P. Bosonization of coupled electron-phonon systems. Zeitschrift für Physik B Condensed Matter 100, 561–565 (1996). https://doi.org/10.1007/s002570050162
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DOI: https://doi.org/10.1007/s002570050162