Spinning Braid Group Representation and the Fractional Quantum Hall Effect

• Main Authors: TING, Hian Ann, Christopher, Lai, C. H.
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 1993
• Subjects: Business
• Online Access: https://ink.library.smu.edu.sg/lkcsb_research/1883; https://doi.org/10.1016/0550-3213(93)90659-D
• Institution: Singapore Management University

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