Spectral Compressibility at the Metal-Insulator Transition of the Quantum Hall Effect

TL;DR

This paper numerically investigates the spectral properties at the metal-insulator transition in the quantum Hall effect, confirming a theoretical relation between spectral compressibility and anomalous diffusion exponent.

Contribution

It introduces a new numerical method using a unitary network model to study spectral properties at the quantum Hall transition, confirming a theoretical relation.

Findings

Confirmed the relation $ ext{spectral compressibility} = ext{anomalous diffusion exponent}/(2d)$ at the transition

Developed a new numerical approach for spectral analysis of disordered systems

Validated theoretical predictions for the quantum Hall delocalization transition

Abstract

The spectral properties of a disordered electronic system at the metal-insulator transition point are investigated numerically. A recently derived relation between the anomalous diffusion exponent $\eta$ and the spectral compressibility $\chi$ at the mobility edge, $\chi=\eta/2d$, is confirmed for the integer quantum Hall delocalization transition. Our calculations are performed within the framework of an unitary network-model and represent a new method to investigate spectral properties of disordered systems.