The Microscopic Picture of Chiral Luttinger Liquid: Composite Fermion Theory of Edge States

TL;DR

This paper develops a microscopic theory for fractional quantum Hall edge states using composite fermions, showing that interactions primarily affect Fermi velocity and justifying the chiral Luttinger liquid model.

Contribution

It provides a microscopic derivation of the chiral Luttinger liquid description of fractional quantum Hall edges via composite fermion theory, including interaction effects.

Findings

Edge states described by Calogero-Sutherland model in 1D limit

Short-range interactions renormalize Fermi velocity only

Microscopic justification of chiral Luttinger liquid model

Abstract

We derive a microscopic theory of the composite fermions describing the low-lying edge excitations in the fractional quantum Hall liquid. Using the composite fermion transformation, one finds that the edge states of the $\nu=1/m$ system in a disc sample are described by, in one dimensional limit, the Calogero-Sutherland model with other interactions between the composite fermions as perturbations. It is shown that a large class of short-range interactions renormalize only the Fermi velocity while the exponent $g=\nu=1/m$ is invariant under the condition of chirality. By taking the sharp edge potential into account, we obtain a microscopic justification of the chiral Luttinger liquid model of the fractional quantum Hall edge states. The approach applied to the $\nu=1/m$ system can be generalized to the other edge states with odd denominator filling factors.