Phase Diagram for a Luttinger Liquid coupled to Phonons in one dimension

TL;DR

This paper analyzes the effects of electron-phonon coupling on a one-dimensional Luttinger liquid, deriving a phase diagram that shows how phonons influence electronic correlations and phase transitions.

Contribution

It provides explicit calculations of Green functions and correlation functions, and establishes a phase diagram for the Hubbard model with phonons, highlighting the impact of the Wentzel-Bardeen singularity.

Findings

Correlation function exponents are sensitive to the Wentzel-Bardeen singularity.

Increasing filling towards half filling can reach the singularity for any phonon coupling.

The system transitions from antiferromagnetic to metallic and then to triplet superconducting phases.

Abstract

The Green function and the ordering correlation functions of a system of electrons coupled to acoustic phonons are calculated explicitly. The sensitivity of the correlation function exponents to the Wentzel-Bardeen singularity is discussed. A phase diagram is established for the Hubbard model coupled to phonons, using the integral equations of Lieb and Wu. By increasing the filling factor towards half filling, the Wentzel-Bardeen singularity can be reached for arbitrary phonon coupling. This suppresses antiferromagnetic fluctuations and drives the system in a metallic phase, and ultimately in the triplet superconducting regime.