Scaling of the localization length in linear electronic and vibrational systems with long-range correlated disorder

TL;DR

This paper develops a scaling theory for localization lengths in disordered chains with long-range correlations, revealing that at low frequencies, correlated chains exhibit shorter localization lengths than uncorrelated ones.

Contribution

It introduces a new scaling theory near the band edge for both electronic and vibrational disordered systems, supported by numerical simulations.

Findings

Localization length is smaller for correlated chains at low frequencies.

Scaling theory successfully maps electronic and vibrational cases.

Numerical simulations confirm theoretical predictions.

Abstract

The localization lengths of long-range correlated disordered chains are studied for electronic wavefunctions in the Anderson model and for vibrational states. A scaling theory close to the band edge is developed in the Anderson model and supported by numerical simulations. This scaling theory is mapped onto the vibrational case at small frequencies. It is shown that for small frequencies, unexpectateley the localization length is smaller for correlated than for uncorrelated chains.