Wentzel-Bardeen singularity and phase diagram for interacting electrons coupled to acoustic phonons in one dimension

TL;DR

This paper investigates how electron-phonon interactions in one-dimensional systems lead to a Wentzel-Bardeen singularity, significantly affecting phase behavior and response functions, including transitions to metallic and triplet superconducting phases.

Contribution

It provides a detailed analysis of the correlation functions and phase diagram for electrons coupled to phonons, highlighting the impact of the Wentzel-Bardeen singularity on phase transitions.

Findings

Correlation functions are highly sensitive to the Wentzel-Bardeen singularity.

Approaching half filling suppresses antiferromagnetic fluctuations.

System transitions from insulating to metallic and then to triplet superconducting phases.

Abstract

Using a Luttinger liquid description, the correlation function exponents of various response functions are calculated. Their striking sensitivity to the non perturbative Wentzel-Bardeen singularity is discussed. For the Hubbard model coupled to phonons, the equivalent of a phase diagram is established. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity is rapidly approached. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.