Explicit Relation of Quantum Hall Effect and Calogero-Sutherland Model

Abstract

Explicit relation between Laughlin state of the quantum Hall effect and one-dimensional(1D) model with long-ranged interaction ($1/r^2$) is discussed. By rewriting lowest Landau level wave functions in terms of 1D representation, Laughlin state can be written as a deformation of the ground state of Calogero-Sutherland model. Corresponding to Laughlin state on different geometries, different types of 1D $1/r^2$ interaction models are derived.

10 pages

References in corpus (4)

• Infinite Symmetry in the Quantum Hall Effect
• Fermions in the Lowest Landau Level: Bosonization, $W_{\infty }$ Algebra, Droplets, Chiral Boson
• The Calogero Model - Anyonic Representation, Fermionic Extension and Supersymmetry
• One-Dimensional Fermions as Two-Dimensional Droplets Via Chern-Simons Theory

Cited by in corpus (69)

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• Dualities in Quantum Hall System and Noncommutative Chern-Simons Theory
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