Quantifying the levitation picture of extended states in lattice models

TL;DR

This paper quantitatively analyzes the behavior of extended states in 2D lattice models, establishing a universal levitation picture and highlighting potential disorder dependence in Quantum Hall phase diagrams.

Contribution

It introduces a quantitative levitation framework for extended states in lattice models, revealing universal behavior and disorder effects in Quantum Hall systems.

Findings

Established a levitation picture for extended states in lattice models

Derived simple expressions for state levitation in continuum limit

Indicated disorder dependence in Quantum Hall phase diagrams

Abstract

The behavior of extended states is quantitatively analyzed for two dimensional lattice models. A levitation picture is established for both white-noise and correlated disorder potentials. In a continuum limit window of the lattice models we find simple quantitative expressions for the extended states levitation, suggesting an underlying universal behavior. On the other hand, these results point out that the Quantum Hall phase diagrams may be disorder dependent.