Various Manifestation of Non -Abelian Statistics in Condensed Matter Systems

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.

Name thesis:degree_name

Ph.D.

Level thesis:degree_level

Dissertation

Grantor

University of Illinois at Urbana-Champaign

Year dc:date

2015

Author dc:creator

• Chung, Suk Bum

Contributors dc:contributor

• Stone, Michael

• Physics, Condensed Matter

Language dc:language

eng

Identifier

(MiAaPQ)AAI3337740

OAI identifier oai:identifier

oai:www.ideals.illinois.edu:2142/87855