Disorder-Induced Vibrational Localization

TL;DR

This paper investigates vibrational localization in disordered systems, identifying critical energies and spectra where vibrational eigenstates transition from extended to localized, and finds universality with electronic localization phenomena.

Contribution

It introduces a detailed analysis of vibrational Anderson localization, connecting vibrational and electronic critical spectra through numerical and analytical methods.

Findings

Critical energy identified for vibrational localization transition

Spectrum at no system-size dependence matches electronic critical spectrum

Universality of critical states extends to vibrational systems

Abstract

The vibrational equivalent of the Anderson tight-binding Hamiltonian has been studied, with particular focus on the properties of the eigenstates at the transition from extended to localized states. The critical energy has been found approximately for several degrees of force-constant disorder using system-size scaling of the multifractal spectra of the eigenmodes, and the spectrum at which there is no system-size dependence has been obtained. This is shown to be in good agreement with the critical spectrum for the electronic problem, which has been derived both numerically and by analytic means. Universality of the critical states is therefore suggested also to hold for the vibrational problem.