Wave function statistics at the symplectic 2D Anderson transition: bulk properties

TL;DR

This study numerically analyzes wavefunction statistics at the 2D Anderson transition with spin-orbit coupling, revealing universal multifractal properties, non-parabolic spectra, and conformal invariance of the critical point.

Contribution

It provides highly accurate critical exponents and uncovers qualitative features of the wavefunction multifractality at the symplectic 2D Anderson transition, supporting universality and conformal invariance.

Findings

Invariance of anomalous dimensions under q→(1-q)

Multifractal spectrum is not parabolic

Critical fixed point exhibits conformal invariance

Abstract

The wavefunction statistics at the Anderson transition in a 2d disordered electron gas with spin-orbit coupling is studied numerically. In addition to highly accurate exponents ($\alpha_0{=}2.172\pm 0.002, \tau_2{=}1.642\pm 0.004$), we report three qualitative results: (i) the anomalous dimensions are invariant under $q\to (1-q)$ which is in agreement with a recent analytical prediction and supports the universality hypothesis. (ii) The multifractal spectrum is not parabolic and therefore differs from behavior suspected, e.g., for (integer) quantum Hall transitions in a fundamental way. (iii) The critical fixed point satisfies conformal invariance.