Correlation of eigenstates in the critical regime of quantum Hall systems

TL;DR

This paper investigates the correlations of eigenstates in quantum Hall systems at criticality, revealing unique multifractal scaling behaviors and supporting the local density of states as an order parameter for the Anderson transition.

Contribution

It extends multifractal analysis by numerically calculating correlations of eigenstates at different energies, uncovering novel scaling relations in quantum Hall critical systems.

Findings

Correlations follow unique multifractal scaling relations.

Critical exponent α₀ ≈ 2.28 characterizes eigenstate behavior.

Supports local density of states as an order parameter.

Abstract

We extend the multifractal analysis of the statistics of critical wave functions in quantum Hall systems by calculating numerically the correlations of local amplitudes corresponding to eigenstates at two different energies. Our results confirm multifractal scaling relations which are different from those occurring in conventional critical phenomena. The critical exponent corresponding to the typical amplitude, $\alpha_0\approx 2.28$, gives an almost complete characterization of the critical behavior of eigenstates, including correlations. Our results support the interpretation of the local density of states being an order parameter of the Anderson transition.