Collective Field Theory of the Fractional Quantum Hall Edge State and the Calogero-Sutherland Model

Abstract

\noindent Using hydrodynamic collective field theory approach we show that one-particle density matrix of the $\nu =1/m$ fractional quantum Hall edge state interpolates between chiral Luttinger liquid behavior $⟨{\psi }^{†}(r)\psi (0)⟩\sim r^{-m}$ and Calogero-Sutherland model behavior $⟨{\psi }^{†}(r)\psi (0)⟩\sim r^{-(m+1/m)/2}$ as the droplet width is varied continuously. Low-energy excitations are described by $c=1$ conformal field theory of a compact boson of radius $\sqrt{m}$. The result suggests complementary relation between the two-dimensional quantum Hall droplet and the one-dimensional Calogero-Sutherland model.

12, UT-682 and SNUTP 94-55#

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• Solitons and giants in matrix models
• Characterization of One-Dimensional Luttinger Liquids in Terms of Fractional Exclusion Statistics
• On Elliptic Algebras and Large-n Supersymmetric Gauge Theories
• Quantum Hydrodynamics from Large-n Supersymmetric Gauge Theories
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• Quantum fluctuations of the Chern-Simons theory and dynamical dimensional reduction
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• Algebra of the observables in the Calogero model and in the Chern-Simons matrix model
• 2D Calogero Model in the Collective-Field Approach
• Exact four-point function and OPE for an interacting quantum field theory with space/time anisotropic scale invariance