Anderson transition in three-dimensional disordered systems with symplectic symmetry

TL;DR

This paper numerically investigates the Anderson transition in three-dimensional disordered systems with symplectic symmetry, estimating the critical exponent and analyzing level statistics at the transition point.

Contribution

It provides the first numerical estimate of the critical exponent for the 3D symplectic Anderson transition and analyzes the critical level statistics, highlighting the role of spin rotation symmetry breaking.

Findings

Critical exponent ν ≈ 1.3 ± 0.2 for the transition

Scale-independent level statistics at the critical point

Distinct energy level spacing distribution from orthogonal ensemble

Abstract

The Anderson transition in a 3D system with symplectic symmetry is investigated numerically. From a one-parameter scaling analysis the critical exponent $\nu$ of the localization length is extracted and estimated to be $\nu = 1.3 \pm 0.2$. The level statistics at the critical point are also analyzed and shown to be scale independent. The form of the energy level spacing distribution $P(s)$ at the critical point is found to be different from that for the orthogonal ensemble suggesting that the breaking of spin rotation symmetry is relevant at the critical point.