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

TL;DR

This paper develops a microscopic theory for edge states in fractional quantum Hall liquids, linking composite fermion models to Calogero-Sutherland models and revealing chiral Luttinger liquid behavior.

Contribution

It derives a microscopic model connecting fractional quantum Hall edge states with Calogero-Sutherland models, extending understanding of edge excitations.

Findings

Reduction to SU(ν*) Calogero-Sutherland model for ν*>0

Ground states can be explicitly found in both cases

Edge excitations exhibit chiral Luttinger liquid behavior

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 $\nu=\frac{\nu^*}{\tilde\phi\nu^*+1}$. For $\nu^*>0$, it is found that the composite fermion model reduces to an SU$(\nu^*)$ Calogero-Sutherland model in the one-dimensional limit, whereas it is not exact soluble for $\nu^*<0$. 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.