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arXiv · hep-th/9202024

Spinning Braid Group Representation and the Fractional Quantum Hall Effect

Christopher Ting·C. H. Lai
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Abstract

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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Christopher Ting, C. H. Lai. 1992-02-07. Spinning Braid Group Representation and the Fractional Quantum Hall Effect. https://doi.org/10.1016/0550-3213(93)90659-d

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