Anderson transition of the plasma oscillations of 1D disordered Wigner lattices

TL;DR

This paper investigates the transition between localized and delocalized plasma oscillations in a 1D disordered Wigner lattice, revealing critical behavior and the effects of different disorder types.

Contribution

It demonstrates a localization-delocalization transition in classical plasma modes of a 1D Wigner Crystal with disorder, including critical scaling laws and the impact of random-bond disorder.

Findings

Localization length diverges at a critical frequency

Power law scaling of critical frequency with interaction strength

All modes localized in a specific disorder realization

Abstract

We report the existence of a localization-delocalization transition in the classical plasma modes of a one dimensional Wigner Crystal with a white noise potential environment at T=0. Finite size scaling analysis reveals a divergence of the localization length at a critical eigenfrequency. Further scaling analysis indicates power law behavior of the critical frequency in terms of the relative interaction strength of the charges. A heuristic argument for this scaling behavior is consistent with the numerical results. Additionally, we explore a particular realization of random-bond disorder in a one dimensional Wigner lattice in which all of the collective modes are observed to be localized.