Geometric scaling in the quantum Hall system

TL;DR

This paper investigates the scaling behavior in the quantum Hall system, revealing an emergent symmetry and proposing effective models that align with observed anti-holomorphic scaling and specific exponents.

Contribution

It introduces a class of effective scaling models based on complex torus structures that explain the observed superuniversal anti-holomorphic scaling in quantum Hall transitions.

Findings

Identification of anti-holomorphic scaling with superuniversal exponents

Proposal of effective models parametrized by complex torus structures

Consistency of model with observed scaling exponent nu = 2.6

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.