Berezinskii-Kosteriltz-Thouless transition in disordered multi-channel Luttinger liquids

TL;DR

This paper investigates the phase transition in disordered multi-channel Luttinger liquids, revealing a Berezinskii-Kosterlitz-Thouless transition influenced by disorder and interactions, with potential observable phases at intermediate temperatures.

Contribution

It derives coupled BKT equations for multi-channel Luttinger liquids and analyzes phase competition, providing new insights into disorder-interaction effects in these systems.

Findings

Identification of BKT transition in multi-channel Luttinger liquids

Demonstration of phase competition between disorder and interactions

Prediction of observable phases at intermediate temperatures

Abstract

We study the phase transition between conducting and insulating states taking place in disordered multi-channel Luttinger liquids with inter-channel interactions. We derive renormalisation group equations which are perturbative in disorder but nonperturbative in interaction. In the vicinity of the simultaneous phase transition in all channels, these equations become a set of coupled Berezinskii--Kosterlitz--Thouless equations, which we analyze within two models: an array of identical wires and a two-channel model with distinct channels. We show that a competition between disorder and interaction results in a variety of phases, expected to be observable at intermediate temperatures where the interaction and disorder are relevant but weak hybridization and the charge-density wave interaction may be ignored.