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

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

1994-06-29

arxiv.org/abs/hep-th/9406192v1

Phys.Lett. B352 (1995) 111-116

Physics

High Energy Physics

High Energy Physics - Theory

12, UT-682 and SNUTP 94-55#

Scientific paper

10.1016/0370-2693(95)00471-V

\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 $\langle \psi^{\dagger}(r) \psi(0) \rangle \sim r^{-m} $ and Calogero-Sutherland model behavior $\langle \psi^{\dagger}(r) \psi(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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