A Microscopic Model of Edge States of Fractional Quantum Hall Liquid: From Composite Fermions to Calogero-Sutherland Model

Abstract

Based on the composite fermion approach, we derive a microscopic theory 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 the one-dimensional limit, 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 since a gap exists between the right- and left-moving sectors in each branch of the azimuthal excitations.