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

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

1993-10-13

arxiv.org/abs/cond-mat/9310027v2

Nucl. Phys. B, 419, 455 (1994)

Physics

Condensed Matter

32 pages, Plain TeX, MIT preprint

Scientific paper

10.1016/0550-3213(94)90340-9

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.

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