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

S. Iso·S. J. Rey
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Abstract

\noindent Using hydrodynamic collective field theory approach we show that one-particle density matrix of the $ν=1/m$ fractional quantum Hall edge state interpolates between chiral Luttinger liquid behavior $\langle ψ^{\dagger}(r) ψ(0) \rangle \sim r^{-m} $ and Calogero-Sutherland model behavior $\langle ψ^{\dagger}(r) ψ(0) \rangle \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.

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S. Iso, S. J. Rey. 1994-06-29. Collective Field Theory of the Fractional Quantum Hall Edge State and the Calogero-Sutherland Model. https://doi.org/10.1016/0370-2693(95)00471-v

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