Statistical, Collective and Critical Phenomena of Classical 1D Disordered Wigner Lattices

TL;DR

This paper investigates the effects of disorder on classical 1D Wigner lattices, analyzing their phase transition, structural properties, quantum fluctuations, and electronic responses, revealing critical phenomena and multifractal characteristics.

Contribution

It provides a comprehensive analysis of disorder effects on 1D Wigner lattices, including phase transition behavior, quantum fluctuation impacts, and multifractal eigenmode properties, which were not fully understood before.

Findings

Disorder induces a transition similar to Anderson localization in plasma modes.

Quantum fluctuations are affected by disorder, altering long-range order.

Eigenmodes exhibit multifractal behavior in disordered Wigner lattices.

Abstract

We explore various properties of classical one-dimensional Wigner solids in the presence of disorder at T=0 in the context of a recently discovered Anderson transition of plasma modes in the random potential system. The extent to which the Wigner lattice is really a ``crystal'' rather than an amorphous solid is discussed for two types of disorder. We investigate the way in which zero point quantum fluctuations that would normally destroy the long range positional order are affected by the disorder. The probability density of particle spacings is examined analytically within a weak disorder approximation and compared to numerical calculations for two different realizations of disorder. We also discuss the multifractal character of the eigenmodes, the compressibility of the electrons, and the AC conductivity.