An Ade-O Classification of Minimal Incompressible Quantum Hall Fluids

TL;DR

This paper classifies minimal incompressible quantum Hall fluids using gauge symmetry, algebraic representations, and quadratic forms, revealing new universality classes with potential physical significance.

Contribution

It introduces a novel classification scheme for quantum Hall fluids based on mathematical structures, expanding the understanding of their universality classes.

Findings

Identification of new universality classes of quantum Hall fluids

Classification for low lattice dimensions N

Insights into the mathematical structure underlying quantum Hall effects

Abstract

We briefly review a theoretical picture of the quantum Hall effect in which gauge symmetry of non-relativistic quantum mechanics, the representation theory of U(1)-current algebra, and the study of odd, positive integral quadratic forms on N-dimensional integral lattices play fundamental roles. We present a classification of so-called minimal incompressible quantum Hall fluids for low values of the lattice dimension N. The classification contains several new universality classes of quantum Hall fluids which are physically interesting.