Spinning Braid Group Representation and the Fractional Quantum Hall Effect
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 op...
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| Main Authors: | , |
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| Format: | text |
| Language: | English |
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Institutional Knowledge at Singapore Management University
1993
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| Subjects: | |
| Online Access: | https://ink.library.smu.edu.sg/lkcsb_research/1883 https://doi.org/10.1016/0550-3213(93)90659-D |
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| Institution: | Singapore Management University |
| Language: | English |
| Summary: | 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 |
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