Off-Diagonal Long Range Order and Scaling in a Disordered Quantum Hall System

TL;DR

This study numerically investigates the bosonic off-diagonal long-range order in disordered quantum Hall systems, revealing its behavior across different phases and its scaling properties, thus enhancing understanding of quantum Hall state ordering.

Contribution

It demonstrates that the bosonic off-diagonal long-range order describes the ordering in disordered quantum Hall states and analyzes its scaling behavior, connecting it to the one-electron Green's function.

Findings

Order parameter vanishes in the disordered phase

Order parameter increases continuously in the ordered phase

Scaling of the order parameter matches that of the one-electron Green's function

Abstract

We have numerically studied the bosonic off-diagonal long range order, introduced by Read to describe the ordering in ideal quantum Hall states, for noninteracting electrons in random potentials confined to the lowest Landau level. We find that it also describes the ordering in disordered quantum Hall states: the proposed order parameter vanishes in the disordered ($\sigma_{xy}=0$) phase and increases continuously from zero in the ordered ($\sigma_{xy}=e^2/h$) phase. We study the scaling of the order parameter and find that it is consistent with that of the one-electron Green's function.