A CLASSIFICATION OF QUANTUM HALL FLUIDS

TL;DR

This paper reviews the classification of quantum Hall fluids using mathematical structures called quantum Hall lattices, discusses their physical implications, and proposes experiments to deepen understanding of the quantum Hall effect.

Contribution

It provides a comprehensive classification of quantum Hall lattices, compares them with experimental data, and suggests new experiments to explore unresolved issues.

Findings

Complete classification of relevant quantum Hall lattices

Comparison with experimental data and hierarchy schemes

Proposals for new experiments to test theoretical predictions

Abstract

In this paper, the key ideas of characterizing universality classes of dissipation-free (incompressible) quantum Hall fluids by mathematical objects called quantum Hall lattices are reviewed. Many general theorems about the classification of quantum Hall lattices are stated and their physical implications are discussed. Physically relevant subclasses of quantum Hall lattices are defined and completely classified. The results are carefully compared with experimental data and also with other theoretical schemes (the hierarchy schemes). Several proposals for new experiments are made which could help to settle interesting issues in the theory of the (fractional) quantum Hall effect and thus would lead to a deeper understanding of this remarkable effect.