Collective field theory of the fractional quantum Hall edge state and the Calogero-Sutherland model

Using the hydrodynamic collective field approximation for the v = 1m fractional quantum Hall droplet dynamics we find that the low-energy excitations are described by c = 1 conformal field theory of a compact boson of radius √m. Using the conformal field theory method we show that the one-particle density matrix of the edge state interpolates between the chiral Luttinger liquid behavior 〈ψ†(r)ψ(0)〉 ∼ r−m and the Calogero-Sutherland model behavior 〈ψ†(r)ψ(0)〉 ∼ r−(m+1m)2 as the droplet width is varied continuously. The result suggests complementary relation between the two-dimensional quantum Hall droplet and the one-dimensional Calogero-Sutherland model.