Correlation Exponent and Anomalously Localized States at the Critical Point of the Anderson Transition

TL;DR

This paper investigates the correlation properties of quantum states at the Anderson transition, demonstrating a key scaling relation after removing anomalously localized states, thus clarifying their influence on critical wavefunction analysis.

Contribution

It confirms the scaling relation between correlation and mass exponents at the Anderson transition after eliminating anomalously localized states, providing new insights into critical wavefunction behavior.

Findings

Confirmed the scaling relation z(q)=d+2tau(q)-tau(2q) for a wide range of q

Demonstrated the influence of anomalously localized states on correlation measurements

Clarified the role of ALS in critical wavefunction analysis

Abstract

We study the box-measure correlation function of quantum states at the Anderson transition point with taking care of anomalously localized states (ALS). By eliminating ALS from the ensemble of critical wavefunctions, we confirm, for the first time, the scaling relation z(q)=d+2tau(q)-tau(2q) for a wide range of q, where q is the order of box-measure moments and z(q) and tau(q) are the correlation and the mass exponents, respectively. The influence of ALS to the calculation of z(q) is also discussed.