{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/87855"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/87855","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Various Manifestation of Non -Abelian Statistics in Condensed Matter Systems","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.","abstract_html":"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.","abstract_has_math":false,"creators":["Chung, Suk Bum"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Stone, Michael"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2015,"date_issued":"2015-09-28T21:55:43Z","date_published":"2015-09-28T21:55:43Z","updated_at":"2026-07-22T22:26:31Z","subjects":["Physics, Condensed Matter"],"languages":["eng"],"rights":[],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["(MiAaPQ)AAI3337740"],"render_values":[{"text":"(MiAaPQ)AAI3337740","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/87855","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Stone, Michael"]},{"key":"dc:creator","label":"Author","values":["Chung, Suk Bum"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2015-09-28T21:55:43Z","10000-01-01","2008"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Ph.D."]},{"key":"thesis:institution_name","label":"Thesis Institution Name","values":["University of Illinois at Urbana-Champaign"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Physics, Condensed Matter"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/87855","(MiAaPQ)AAI3337740"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["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.","Made available in DSpace on 2015-09-28T21:55:43Z (GMT). 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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.","Made available in DSpace on 2015-09-28T21:55:43Z (GMT). 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