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
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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