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 (19)

• Novel Symmetry Classes in Mesoscopic Normal-Superconducting Hybrid Structures
• Riemannian symmetric superspaces and their origin in random matrix theory
• Conformal Field Theory of AdS Background with Ramond-Ramond Flux
• Exact relations between multifractal exponents at the Anderson transition
• gl(N|N) Super-Current Algebras for Disordered Dirac Fermions in Two Dimensions
• Two-dimensional conformal field theory for disordered systems at criticality
• $PSL(n|n)$ Sigma Model as a Conformal Field Theory
• Multifractality of wavefunctions at the quantum Hall transition revisited
• Multifractality at the quantum Hall transition: Beyond the parabolic paradigm
• Towards a Field Theory of the Plateau Transition
• The WZNW model on PSU(1,1|2)
• Point-Contact Conductances at the Quantum Hall Transition
• Surface criticality and multifractality at localization transitions
• Magnetic properties of Sr_2Fe_1+xMo_1-xO_6 with -1 <= x <= 0.25
• Multifractality and Conformal Invariance at 2D Metal-Insulator Transition in the Spin-Orbit Symmetry Class
• Network models for localisation problems belonging to the chiral symmetry classes
• Evidence for the PSL(2$|$2) Wess-Zumino-Novikov-Witten model as a model for the plateau transition in Quantum Hall effect: Evaluation of numerical simulations
• Point-Contact Conductances from Density Correlations
• Corner Multifractality for Reflex Angles and Conformal Invariance at 2D Anderson Metal-Insulator Transition with Spin-Orbit Scattering

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