Chiral Operator Product Algebra and Edge Excitations of a Fractional Quantum Hall Droplet

TL;DR

This paper explores the edge excitations of fractional quantum Hall droplets using conformal field theory, proposing a bulk-edge correspondence via chiral operator product algebra and confirming predictions with numerical results.

Contribution

It introduces a classification of edge state spectra through chiral operator product algebra, linking bulk properties with edge excitations in non-abelian FQH systems.

Findings

Good agreement between numerical edge state counts and chiral OPA predictions

Edge specific heat calculations for non-abelian FQH states

Proposal of a bulk-edge correspondence using CFT techniques

Abstract

In this paper we study the spectrum of low-energy edge excitations of a fractional quantum Hall (FQH) droplet. We show how to generate, by conformal field theory (CFT) techniques, the many-electron wave functions for the edge states. And we propose to classify the spectrum of the edge states by the same chiral operator product algebra (OPA) that appears in the CFT description of the ground state in the bulk. This bulk-edge correspondence is suggested particularly for FQH systems that support quasiparticle obeying non-abelian braid statistics, including the $\nu=5/2$ Haldane-Rezayi state. Numerical diagonalization to count the low-lying edge states has been done for several non-abelian FQH systems, showing good agreement in all cases with the chiral OPA predictions. The specific heat of the edge excitations in those non-abelian states is also calculated.