Geometric scaling in the quantum Hall system
Mesoscale and Nanoscale Physics
2009-11-13 v1
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.
Cite
@article{arxiv.0706.2467,
title = {Geometric scaling in the quantum Hall system},
author = {C. A. Lutken and G. G. Ross},
journal= {arXiv preprint arXiv:0706.2467},
year = {2009}
}