The Microscopic Model of Composite Fermion Type Excitations for \nu=1/m Edge States

TL;DR

This paper develops a microscopic theory for edge excitations in fractional quantum Hall systems at filling factor 1/m, showing they behave as chiral Luttinger liquids and are described by a Calogero-Sutherland-like model.

Contribution

It introduces a microscopic model linking composite fermion excitations to a one-dimensional Calogero-Sutherland-like model for fractional quantum Hall edge states.

Findings

Edge states are described by a CSLM in the 1D limit.

Low-lying excitations exhibit chiral Luttinger liquid behavior.

There is a gap between right- and left-moving excitations.

Abstract

We derive a microscopic theory of the composite fermion type quasiparticles describing the low-lying edge excitations in the fractional quantum Hall liquid with $\nu=1/m$. Using the composite fermion transformation, one finds that the edge states of the system in a disc sample are described by the Calogero-Sutherland-like model (CSLM) in the one-dimensional limit. This result presents the consistency between one-dimensional and two-dimensional statistics. It is shows that the low-lying excitations, indeed, have the chiral Luttinger liquid behaviors because there is a gap between the right- and left-moving excitations of the CSLM.