Quantum and classical localization in the lowest Landau level

TL;DR

This paper demonstrates that quantum effects in the lowest Landau level influence localization properties, revealing a quantum analog of classical percolation and suggesting new experimental quantum critical points.

Contribution

It introduces the quantum analog of classical percolation effects in the lowest Landau level and confirms the applicability of the extended Harris criterion to quantum localization.

Findings

Quantum correlations affect localization critical exponents.

Extended Harris criterion applies to quantum localization in LLL.

Potential for new quantum critical points in experiments.

Abstract

Spatial correlations of occupation probabilities, if their decay is not too fast, can change the critical exponents for classical percolation. From numerical studies of electron dynamics in the lowest Landau level (LLL) we demonstrate the quantum analog of this effect. Similar to classical percolation, we find that the extended Harris criterion applies to localization in the LLL. These results suggest experiments that might probe new quantum critical points in the integer quantum Hall setting.