Fusion and tensoring of conformal field theory And composite fermion picture of fractional quantum hall effect

authored by

Michael A.I. Flohr

Abstract

We propose a new way for describing the transition between two quantum Hall effect states with different filling factors within the framework of rational conformal field theory. Using a particular class of nonunitary theories, we explicitly recover Jain's picture of attaching flux quanta by the fusion rules of primary fields. Filling higher Landau levels of composite fermions can be described by taking tensor products of conformal theories. The usual projection to the lowest Landau level corresponds then to a simple coset of these tensor products with several U(1)-theories divided out. These two operations -the fusion map and the tensor map - can explain the Jain series and all other observed fractions as exceptional cases. Within our scheme of transitions we naturally find a field with the experimentally observed universal critical exponent 7/3.

External Organisation(s)

Spanish National Research Council (CSIC)
Institute for Advanced Study (IAS)

Type

Article

Journal

Modern Physics Letters A

Volume

11

Pages

55-68

No. of pages

14

ISSN

0217-7323

Publication date

1996

Publication status

Published

Peer reviewed

Yes

ASJC Scopus subject areas

Nuclear and High Energy Physics, Astronomy and Astrophysics, General Physics and Astronomy

Electronic version(s)

https://doi.org/10.48550/arXiv.hep-th/9605152 (Access: Open)
https://doi.org/10.1142/S0217732396000084 (Access: Closed)