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

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

1993-10-27

arxiv.org/abs/hep-th/9310181v1

Phys.Rev.Lett. 72 (1994) 1902-1905

Physics

High Energy Physics

High Energy Physics - Theory

11 pages, RevTeX 3.0, MPI-Ph/93-75 DFTT 65/93

Scientific paper

10.1103/PhysRevLett.72.1902

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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