A perturbative study of delocalisation transition in one-dimensional models with long-range correlated disorder

TL;DR

This paper investigates how long-range correlations in disorder induce a delocalisation transition in one-dimensional systems, revealing a change in the scaling law of the inverse localisation length from quadratic to quartic at the transition.

Contribution

It introduces a perturbative method to analyze the delocalisation transition in 1D models with correlated disorder, highlighting a new scaling law change.

Findings

The inverse localisation length changes from quadratic to quartic scaling at the transition.

Long-range correlations in disorder can induce a delocalisation transition in 1D systems.

The transition is characterized by a specific change in the scaling law of the inverse localisation length.

Abstract

We study the delocalisation transition which takes places in one-dimensional disordered systems when the random potential exhibits specific long-range correlations. We consider the case of weak disorder; using a systematic perturbative approach, we show how the delocalisation transition brings about a change of the scaling law of the inverse localisation length which ceases to be a quadratic function of the disorder strength and assumes a quartic form when the threshold separating the localised phase from the extended one is crossed.