Chiral Operator Product Algebra Hidden in Certain Fractional Quantum Hall Wave Functions

TL;DR

This paper explores how certain fractional quantum Hall wave functions can be understood through their underlying conformal field theory operator algebra, revealing non-abelian topological order and aiding in quasi-particle characterization.

Contribution

It demonstrates how to derive the conformal field theory operator algebra from specific FQH wave functions, including new states like d-wave paired states, to understand their topological order.

Findings

Uncovered chiral operator product algebra in FQH states

Connected FQH wave functions to CFT correlation functions

Characterized non-abelian topological order through operator algebra

Abstract

In this paper we study the conditions under which an N-electron wave function for a fractional quantum Hall (FQH) state can be viewed as N-point correlation function in a conformal field theory (CFT). Several concrete examples are presented to illustrate, when these condition are satisfied, how to ``derive'' or ``uncover'' relevant operator algebra in the associated CFT from the FQH wave function. Besides the known Pfaffian state, the states studied here include three d-wave paired states, one for spinless electrons and two for spin-1/2 electrons (one of them is the Haldane-Rezayi state). It is suggested that the non-abelian topological order hidden in these states can be characterized by their associated chiral operator product algebra, from which one may infer the quantum numbers of quasi-particles and calculate their wave functions.