Wentzel-Bardeen singularity in coupled Luttinger liquids: transport properties

TL;DR

This paper reviews how the Wentzel-Bardeen singularity influences transport in strongly correlated one-dimensional electron systems coupled to phonons, revealing phase transitions and regimes via renormalization group analysis.

Contribution

It introduces a detailed analysis of the Wentzel-Bardeen singularity's role in 1D electron-phonon systems and its impact on transport properties and phase behavior.

Findings

The singularity suppresses antiferromagnetic fluctuations.

It induces a transition toward a metallic phase.

Three transport regimes are identified through response function divergence.

Abstract

The recent progress on 1 D interacting electrons systems and their applications to study the transport properties of quasi one dimensional wires is reviewed. We focus on strongly correlated electrons coupled to low energy acoustic phonons in one dimension. The Wentzel--Bardeen singularity suppresses antiferromagnetic fluctuations and pushes the system toward the metallic phase via an intermediate, metallic phase. The implications of this phenomenon on the transport properties of an ideal wire as well as the properties of a wire with weak or strong scattering are analyzed in a perturbative renormalization group calculation. This allows to recover the three regimes predicted from the divergence criteria of the response functions.