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Aspects of Non-Abelian Many Body Physics


Bradford, Kent B. (1997) Aspects of Non-Abelian Many Body Physics. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/rn7x-3882.


The general formulation of quantum statistical mechanics hints at interesting generalizations of the usual Bose/Fermi framework in two spatial dimensions. Anyon statistics, which is essentially a continuous interpolation between Bose and Fermi statistics, is relevant to the Fractional Quantum Hall Effect in two-dimensional (i.e., thin layer) condensed matter systems. In addition, the possibility of non-abelian statistics, in which the multi-particle wavefunction transforms as a representation of a non-abelian group under the exchange of indistinguishable particles, has been explored. Spontaneously broken non-abelian gauge theories in (2 + 1) dimensions often have stable topological defects, called non-abelian vortices, that experience non-abelian statistics. In addition, it has been suggested that degenerate quasihole multiplets in Quantum Hall systems also transform as non-abelian representations of the braid group under particle exchange. In this thesis, I explore the braiding properties of systems of two-cycle flux vortices in a residual S₃ discrete gauge group. The individual vortices are uncharged, but multi-vortex states can have Cheshire charge. The uncharged sectors all have non-vanishing bosonic subspaces, as do the non-abelian charged trivial flux sectors. A kinetic Hamiltonian for vortices on a periodic lattice is constructed. There is a modification to the translational symmetry in the periodically identified direction for non-trivial Z₂ charged sectors. The ground state energies for various three and four vortex sectors is numerically determined. Typically, the ground state is bosonic, with a gap separating it from a non-abelian subspace.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:Physics
Degree Grantor:California Institute of Technology
Division:Physics, Mathematics and Astronomy
Major Option:Physics
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Preskill, John P.
Thesis Committee:
  • Preskill, John P. (chair)
  • Politzer, Hugh David
  • Wise, Mark B.
  • Weichman, Peter B.
Defense Date:23 May 1997
Other Numbering System:
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Record Number:CaltechTHESIS:11192019-171459529
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:13579
Deposited By: Mel Ray
Deposited On:20 Nov 2019 01:32
Last Modified:19 Apr 2021 22:32

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