From Composite Fermions to Calogero-Sutherland Model: Edge of Fractional Quantum Hall Liquid and the Dimension Reduction

Abstract

We derive a microscopic model describing the low-lying edge excitations in the fractional quantum Hall liquid with $ν=\frac{ν^*} {\tildeϕν^*+1}$. For $ν^*>0$, it is found that the composite fermion model reduces to an SU$(ν^*)$ Calogero-Sutherland model in a dimension reduction, whereas it is not exact soluble for $ν^*<0$. However, the ground states in both cases can be found and the low-lying excitations can be shown the chiral Luttinger liquid behaviors. On the other hand, we shows that the finite temperature behavior of $G-T$ curve will deviate from the prediction of the chiral Luttinger liquid. We also point out that the suppression of the `spin&#39; degrees of freedom agrees with very recent experiments by Chang et al. The two-boson model of Lee and Wen is described microscopically.