Exact exponents for the spin quantum Hall transition in the presence of multiple edge channels

Abstract

Critical properties of quantum Hall systems are affected by the presence of extra edge channels - 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.

5 pages and 4 page supplemental material, 4 figures

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• Rectangular amplitudes, conformal blocks, and applications to loop models
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• Quantum Hall transitions: An exact theory based on conformal restriction
• Transport through the network of topological channels in HgTe based quantum well
• Statistics of Conductances and Subleading Corrections to Scaling near the Integer Quantum Hall Plateau Transition
• Generalized surface multifractality in 2D disordered systems
• Phase diagram and the strong-coupling fixed point in the disordered O(n) loop model
• Generalized multifractality at the spin quantum Hall transition: Percolation mapping and pure-scaling observables