Electron-phonon coupling close to a metal-insulator transition in one dimension

TL;DR

This paper analyzes the role of electron-phonon interactions near a metal-insulator transition in a one-dimensional system, showing that low-momentum phonons are generally irrelevant unless strongly coupled, despite reduced carrier velocity.

Contribution

It demonstrates that low-momentum phonons do not significantly influence the transition unless their coupling strength is large, clarifying their role in one-dimensional electron systems.

Findings

Low-momentum phonons are irrelevant near the transition unless strongly coupled.

The metal-insulator transition can be described as an incommensurate to commensurate transition.

Carrier velocity diminishes without increasing the effective electron-phonon coupling.

Abstract

We consider a one-dimensional system of electrons interacting via a short-range repulsion and coupled to phonons close to the metal-insulator transition at half filling. We argue that the metal-insulator transition can be described as a standard one dimensional incommensurate to commensurate transition, even if the electronic system is coupled to the lattice distortion. By making use of known results for this transition, we prove that low-momentum phonons do not play any relevant role close to half-filling, unless their coupling to the electrons is large in comparison with the other energy scales present in the problem. In other words the effective strength of the low-momentum transferred electron-phonon coupling does not increase close to the metal-insulator transition, even though the effective velocity of the mobile carriers is strongly diminished.