From composite fermions to the Calogero-Sutherland model: Edge of the fractional quantum Hall liquid and the dimension reduction

We derive a microscopic model describing low-lying edge excitations in a fractional quantum Hall liquid with ν=ν^*/(φ̃ν^*+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 exactly soluble for ν^*<0. However, the ground states in both cases can be found, and the low-lying excitations can show chiral Luttinger-liquid behaviors. On the other hand, we show that the finite-temperature behavior of the G-T curve will deviate from the prediction of the chiral Luttinger liquid. We also point out that the suppression of the “spin” degrees of freedom agrees with very recent experiments by Chang et al. [Phys. Rev. Lett. 77, 2538 (1996)]. The two-boson model of Lee and Wen (preprint, cond-mat/9801318) is described microscopically.