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
Citation
TING, Hian Ann, Christopher and Lai, C. H..
Spinning Braid Group Representation and the Fractional Quantum Hall Effect. (1993). Nuclear Physics B. 396, (2-3), 429-464.
Available at: https://ink.library.smu.edu.sg/lkcsb_research/1883
