Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry

TL;DR

This paper presents an algebraic classification of quantum Hall states using the $ ext{W}_{1+ ext{infinity}}$ symmetry, linking edge conformal field theories to incompressible quantum fluids and their excitations.

Contribution

It introduces a novel algebraic framework based on $ ext{W}_{1+ ext{infinity}}$ algebra for classifying all hierarchical quantum Hall states, including measured fractions.

Findings

Complete algebraic classification of hierarchical quantum Hall states.

All measured fractional quantum Hall states are encompassed.

Spin-polarized electrons exhibit Abelian anyon excitations.

Abstract

We show how two-dimensional incompressible quantum fluids and their excitations can be viewed as $\ W_{1+\infty}\ $ edge conformal field theories, thereby providing an algebraic characterization of incompressibility. The Kac-Radul representation theory of the $\ W_{1+\infty}\ $ algebra leads then to a purely algebraic complete classification of hierarchical quantum Hall states, which encompasses all measured fractions. Spin-polarized electrons in single-layer devices can only have Abelian anyon excitations.