Exact Exponents for the Spin Quantum Hall Transition in the Presence of Multiple Edge Channels

2011/09/30 by Roberto Bondesan, Ilya A. Gruzberg, Jesper Lykke Jacobsen +2 · 13 citations
Mathematics · Physics and Astronomy · #Computer science #Condensed matter physics #Critical exponent #Electron #Enhanced Data Rates for GSM Evolution #Fractional quantum Hall effect #Mathematics #Phase transition #Physics #Physics of Superconductivity and Magnetism #Plateau (mathematics) #Quantum #Quantum Hall effect #Quantum and electron transport phenomena #Quantum many-body systems #Quantum mechanics #Quantum spin Hall effect #Spin (aerodynamics) #cond-mat.dis-nn #cond-mat.mes-hall

paper · pdf · doi:10.1103/physrevlett.108.126801

published in Physical Review Letters 108(12), 126801 (American Physical Society) · 5 pages and 4 page supplemental material, 4 figures

arxiv created 2012/03/19 · openalex publication_date 2012/03/19 · arxiv updated 2012/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

Critical properties of quantum Hall systems are affected by the presence of extra edge channels-those that are present, in particular, at higher plateau transitions. We study this phenomenon for the case of the spin quantum Hall transition. Using supersymmetry, we map the corresponding network model to a classical loop model, whose boundary critical behavior was recently determined exactly. We verify predictions of the exact solution by extensive numerical simulations.

Citations

• Boundary multifractality in critical one-dimensional systems with long-range hopping
• 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
• Boundary criticality at the Anderson transition between a metal and a quantum spin Hall insulator in two dimensions
• Quantum Hall Plateau Transitions in Disordered Superconductors
• Charge accumulation at the boundaries of a graphene strip induced by a gate voltage: Electrostatic approach
• Multifractality at the Quantum Hall Transition: Beyond the Parabolic Paradigm
• Percolation, quantum tunnelling and the integer Hall effect
• Scaling and crossover functions for the conductance in the directed network model of edge states
• Magnetic properties of Sr₂Fe₁+xMo₁-xO₆ with -1 <= x <= 0.25