Algebraic Aspects of the Fractional Quantum Hall Effect

Abstract

Some algebraic issues of the FQHE are presented. First, it is shown that on the space of Laughlin wavefunctions describing the $\nu =1/m$ FQHE, there is an underlying $W_{\infty }$ algebra, which plays the role of a spectrum generating algebra and expresses the symmetry of the ground state. Its generators are expressed in a second quantized language in terms of fermion and vortex operators. Second, we present the naturally emerging algebraic structure once a general two-body interaction is introduced and discuss some of its properties.

22 pages, SU-4240-553

References in corpus (6)

• Infinite Symmetry in the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• Conformal Symmetry and Universal Properties of Quantum Hall States
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory
• W-Infinity and String Theory
• Large N Limit in the Quantum Hall Effect

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• Duality and the Fractional Quantum Hall Effect
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Numerical Study of Hierarchical Hall Edge States on the Disk Geometry
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• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
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• 2D Superconductivity: Classification of Universality Classes by Infinite Symmetry
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• Semiclassical Droplet States in Matrix Quantum Hall Effect
• On a New Universal Class of Phase Transitions and Quantum Hall Effect
• Noncommutative Solitons and the W_{1+\infty} Algebras in Quantum Hall Theory
• Geometric Transformations and NCCS Theory in the Lowest Landau Level
• Chern-Simons Theory and Quantum Fields in the Lowest Landau Level
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect