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Anyonization and novel braid structure in dumb-bell Chern-Simons theory

Authors
Journal
Physics Letters B
0370-2693
Publisher
Elsevier
Publication Date
Volume
266
Identifiers
DOI: 10.1016/0370-2693(91)91054-y

Abstract

Abstract We discuss a novel version of lattice Chern-Simons theory which has a natural coupling to extended “dumb-bell” matter. We show that the Chern-Simons term is parity and time-reversal invariant and can be coupled to matter in a P and T invariant way. We also show that the coupling to dumb-bells breaks P and T invariance and that dumb-bells are anyons. The physical states of the dumb-bell theory represent a version of the braid group of R 2 which gives them the usual monodromy of anyon states as well as fractional spin satisfying the natural spin-statistics relation. The continuum limit is treated and, by eliminating extra degrees of freedom, is shown to be precisely equivalent to ordinary Chern-Simons theory.

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