Bosonization of coupled electron-phonon systems

TL;DR

This paper uses higher dimensional bosonization to analyze electron-phonon systems, revealing that Coulomb interactions do not destabilize Fermi liquids in 3D and that 3D Luttinger liquid behavior can arise from anisotropic band structures or phonon frequencies.

Contribution

It introduces a non-perturbative bosonization method for coupled electron-phonon systems that does not assume Fermi liquid behavior, providing new insights into 3D electronic states.

Findings

Long-range Coulomb interactions do not destabilize Fermi liquids in 3D.

Strong electron-phonon coupling results in small quasi-particle residues.

3D Luttinger liquid behavior can originate from anisotropy in electronic bands or phonon frequencies.

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}}.