Boundary multifractality at the integer quantum Hall plateau transition: implications for the critical theory

TL;DR

This paper investigates the multifractal spectra of wave functions at the integer quantum Hall transition, revealing non-parabolic spectra and boundary-to-bulk exponent ratios, challenging existing theoretical models.

Contribution

It provides new numerical constraints on critical theories, demonstrating non-parabolic multifractal spectra and exact boundary spectrum parabolicity in a related symmetry class.

Findings

Non-parabolic multifractal spectrum at the transition

Boundary-to-bulk multifractal exponent ratio determined

Analytic proof of parabolic boundary spectra in Gade-Wegner class

Abstract

We study multifractal spectra of critical wave functions at the integer quantum Hall plateau transition using the Chalker-Coddington network model. Our numerical results provide important new constraints which any critical theory for the transition will have to satisfy. We find a non-parabolic multifractal spectrum and we further determine the ratio of boundary to bulk multifractal exponents. Our results rule out an exactly parabolic spectrum that has been the centerpiece in a number of proposals for critical field theories of the transition. In addition, we demonstrate analytically exact parabolicity of related boundary spectra in the 2D chiral orthogonal `Gade-Wegner' symmetry class.