Various Manifestation of Non -Abelian Statistics in Condensed Matter Systems
Chung, Suk Bum
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https://hdl.handle.net/2142/87855
Description
Title
Various Manifestation of Non -Abelian Statistics in Condensed Matter Systems
Author(s)
Chung, Suk Bum
Issue Date
2008
Doctoral Committee Chair(s)
Stone, Michael
Degree Granting Institution
University of Illinois at Urbana-Champaign
Degree Name
Ph.D.
Degree Level
Dissertation
Date of Ingest
2015-09-28T21:55:43Z
Keyword(s)
Physics, Condensed Matter
Language
eng
Abstract
Since fractional statistics of Laughlin states is reflected in its topological degeneracy, it is natural to expect non-Abelian statistics to have some effect on topological degeneracy. To study the topological degeneracy of the Moore-Read nu = 5/2 quantum Hall state on a torus, we construct the wave functions of this state in the presence of two quasiholes [6]. These explicit wave functions allow us to compute the monodromy matrix that describes the effect of quasihole motion on the space of degenerate ground states. Our calculation provides a conformal field theory explanation of why certain transitions between ground states are forbidden. It is because taking a quasihole around a generator of the torus can change the fusion channel of the two quasiholes, and this requires a change of parity of the electron number in sonic of the ground states.
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