Spinning Braid Group Representation and the Fractional Quantum Hall Effect

Details Spinning Braid Group Representation and the Fractional Quantum Hall Effect Spinning Braid Group Representation and the Fractional Quantum Hall Effect

1992-02-07

arxiv.org/abs/hep-th/9202024v1

Nucl.Phys. B396 (1993) 429-464

Physics

High Energy Physics

High Energy Physics - Theory

(36 pages) e-mail scip1005@nusvm.bitnet

Scientific paper

10.1016/0550-3213(93)90659-D

The path integral approach to representing braid group is generalized for particles with spin. Introducing the notion of {\em 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 {\em 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 {\em 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.

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