Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class

TL;DR

This paper investigates the multifractality of wave functions at the 2D metal-insulator transition in the spin-orbit class, providing numerical evidence for conformal invariance and boundary effects on multifractal properties.

Contribution

It demonstrates that boundary and corner multifractal exponents differ from bulk values and are related through conformal invariance, confirming conformal invariance at the transition.

Findings

Boundary multifractal exponents differ from bulk.

Corner exponents relate to boundary exponents via conformal invariance.

Boundaries influence the entire sample's multifractality in the thermodynamic limit.

Abstract

We study the multifractality (MF) of critical wave functions at boundaries and corners at the metal-insulator transition (MIT) for noninteracting electrons in the two-dimensional (2D) spin-orbit (symplectic) universality class. We find that the MF exponents near a boundary are different from those in the bulk. The exponents at a corner are found to be directly related to those at a straight boundary through a relation arising from conformal invariance. This provides direct numerical evidence for conformal invariance at the 2D spin-orbit MIT. The presence of boundaries modifies the MF of the whole sample even in the thermodynamic limit.