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

A. Cappelli·C. A. Trugenberger·G. R. Zemba
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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.

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A. Cappelli, C. A. Trugenberger, G. R. Zemba. 1993-10-27. Classification of Quantum Hall Universality Classes by $\ W_{1+\infty}\ $ symmetry. https://doi.org/10.1103/physrevlett.72.1902

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