Spinning Braid Group Representation and the Fractional Quantum Hall Effect

Publication Type

Journal Article

Publication Date

1993

Abstract

The path-integral approach to representing braid group is generalized for particles with spin. Introducing the notion of charged winding number in the super-plane, we represent the braid-group generators as homotopically constrained Feynman kernels. In this framework, super Knizhnik-Zamolodchikov operators appear naturally in the hamiltonian, suggesting the possibility of spinning nonabelian anyons. We then apply our formulation to the study of fractional quantum Hall effect (FQHE). A systematic discussion of the ground states and their quasi-hole excitations is given. We obtain Laughlin, Halperin and Moore-Read states as exact ground-state solutions to the respective hamiltonians associated to the braid-group representations. The energy gap of the quasi-excitation is also obtainable from this approach

Discipline

Business

Research Areas

Quantitative Finance

Publication

Nuclear Physics B

Volume

396

Issue

2-3

First Page

429

Last Page

464

ISSN

0550-3213

Identifier

10.1016/0550-3213(93)90659-D

Publisher

Elsevier

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