$W_{\infty }$ Algebras in the Quantum Hall Effect

Abstract

We show that a large class of incompressible quantum Hall states correspond to different representations of the \Winf algebra by explicit construction of the second quantized generators of the algebra in terms of fermion and vortex operators. These are parametrized by a set of integers which are related to the filling fraction. The class of states we consider includes multilayer Hall states and the states proposed by Jain to explain the hierarchical filling fractions. The corresponding second quantized order parameters are also given.

18 pages, SU-4240-580 (correction in equation (4.2))

References in corpus (9)

• 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
• Classification of Quantum Hall Universality Classes by $W_{1+\infty }$ symmetry
• Large N Limit in the Quantum Hall Effect
• W_{\infty} Gauge Transformations and the Electromagnetic Interactions of Electrons in the Lowest Landau Level
• Algebraic Aspects of the Fractional Quantum Hall Effect
• Infinite Symmetry in the Fractional Quantum Hall Effect

Cited by in corpus (21)

• Band geometry of fractional topological insulators
• Quantum Hall Effect in Higher Dimensions, Matrix Models and Fuzzy Geometry
• Stable Hierarchical Quantum Hall Fluids as W-(1 + infinity) Minimal Models
• Updating QCD${}_2$
• LLL vs. LLM: Half BPS Sector of N=4 SYM Equals to Quantum Hall System
• Collective Field Theory of the Fractional Quantum Hall Edge State and the Calogero-Sutherland Model
• Duality and the Fractional Quantum Hall Effect
• Hamiltonian Formulation of the W-Infinity Minimal Models
• Matrix Model Description of Laughlin Hall States
• Bosonization of the lowest Landau level in arbitrary dimensions: edge and bulk dynamics
• Physics on the edge: contour dynamics, waves and solitons in the quantum Hall effect
• W-infinity Symmetry in the Quantum Hall Effect Beyond the Edge
• Geometric quench in the fractional quantum Hall effect: exact solution in quantum Hall matrix models and comparison with bimetric theory
• W(infty)-Covariance of the Weyl-Wigner-Groenewold-Moyal Quantization
• 2D Superconductivity: Classification of Universality Classes by Infinite Symmetry
• The Renormalization Group and Quantum Hall Edge States
• Ordered Products, $W_{\infty }$-Algebra, and Two-Variable, Definite-Parity, Orthogonal Polynomials
• Spinor Field Realizations of the half-integer $W_{2,s}$ Strings
• Physical States and BRST Operators for Higher-spin $W$ Strings
• Holomorphicity, Vortex Attachment, Gauge Invariance and the Fractional Quantum Hall Effect
• Explicit field realizations of W algebras