Geometric scaling in the quantum Hall system

Abstract

The transitions between neighbouring plateaux in the quantum Hall system are observed to follow anti-holomophic scaling with superuniversal scaling exponents, showing that the system contains an emergent sub-modular discrete symmetry and a holomorphic structure at low energies. We identify a class of effective scaling models consistent with this data, which is parametrized by the complex structure of a torus with a special spin structure, in which only the number of fermions (c) remains undetermined. For c = 2 this gives the superuniversal anti-holomorphic scaling potential previously inferred from data, with scaling exponent nu = 2.6, in reasonable agreement with available scaling data.

6 pages

References in corpus (3)

• Scaling Theory of the Integer Quantum Hall Effect
• Corrections to Scaling in the Integer Quantum Hall Effect
• One-Dimensional Flows in the Quantum Hall System

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• Green's functions on a renormalized lattice: An improved method for the integer quantum Hall transition
• An RG potential for the quantum Hall effects
• Duality and modular symmetry in the quantum Hall effect from Lifshitz holography
• Elliptic mirror of the quantum Hall effect