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

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.

4 pages, 3 figures, v2, published version

References in corpus (3)

• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Corner Multifractality for Reflex Angles and Conformal Invariance at 2D Anderson Metal-Insulator Transition with Spin-Orbit Scattering

Cited by in corpus (9)

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• Critical exponent for the quantum Hall transition
• Multifractal analysis with the probability density function at the three-dimensional Anderson transition
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model I: Symmetry relation under typical averaging
• Multifractal analysis of the metal-insulator transition in the 3D Anderson model II: Symmetry relation under ensemble averaging
• Statistics of renormalized on-site energies and renormalized hoppings for Anderson localization models in dimensions d=2 and d=3
• Point-Contact Conductance in Asymmetric Chalker-Coddington Network Model
• Anderson transitions : multifractal or non-multifractal statistics of the transmission as a function of the scattering geometry