Anomalously localized states and multifractal correlations of critical wavefunctions in two-dimensional electron systems with spin-orbital interactions

TL;DR

This paper investigates anomalously localized states at the critical point of the Anderson transition in 2D electron systems with spin-orbital interactions, revealing their finite probability and impact on critical properties.

Contribution

It provides a quantitative definition of ALS, analyzes their system-size dependence, and demonstrates their effect on the distribution of critical wavefunction properties.

Findings

ALS probability increases with system size

ALS exist with finite probability even in infinite systems

Eliminating ALS sharpens the distribution of correlation dimensions

Abstract

Anomalously localized states (ALS) at the critical point of the Anderson transition are studied for the SU(2) model belonging to the two-dimensional symplectic class. Giving a quantitative definition of ALS to clarify statistical properties of them, the system-size dependence of a probability to find ALS at criticality is presented. It is found that the probability increases with the system size and ALS exist with a finite probability even in an infinite critical system, though the typical critical states are kept to be multifractal. This fact implies that ALS should be eliminated from an ensemble of critical states when studying critical properties from distributions of critical quantities. As a demonstration of the effect of ALS to critical properties, we show that the distribution function of the correlation dimension of critical wavefunctions becomes a delta function in the thermodynamic limit only if ALS are eliminated.