{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/99304"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/99304","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Anyonic symmetry and twist defects","abstract":"Non-Abelian excitations are sought after because of the promise they hold for topological quantum computation. However, in spite of many proposals of systems in which they can occur intrinsically, observation has proved to be elusive. In this thesis, we study ways in which we can engineer such excitations by combining two parent Abelian theories, and as a result allow for defects which host non-Abelian zero modes. We first formulate the symmetries of the anyonic excitations of Abelian topological states. Then, we study properties of semiclassical point defects, called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. Non-Abelian twist defects appear between different gapped phases. We study the twist defects for a variety of bosonic ADE fractional quantum spin Hall systems for which the anyonic symmetries turn out to be given by their Dynkin diagrams. We also look at superconducting heterostructures with fermionic quantum Hall states and show the presence of anyonic symmetries and twist defects which physically correspond to a fermion parity flip. This can result in Majorana bound states at such defects instead of more exotic parafermions as was believed before. This is because the presence of the superconductor necessitates the consideration of a larger bosonic topological order. We then investigate the twist defects further by promoting the anyonic symmetries from global to local. This deconfines the defects and results in non-Abelian topological states called twist liquids. Finally, we study the emergence of new topological order from two constituent systems driven by the condensation of a composite boson. This allows us to study a variety of systems with non-Abelian excitations.","abstract_html":"Non-Abelian excitations are sought after because of the promise they hold for topological quantum computation. However, in spite of many proposals of systems in which they can occur intrinsically, observation has proved to be elusive. In this thesis, we study ways in which we can engineer such excitations by combining two parent Abelian theories, and as a result allow for defects which host non-Abelian zero modes. We first formulate the symmetries of the anyonic excitations of Abelian topological states. Then, we study properties of semiclassical point defects, called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. Non-Abelian twist defects appear between different gapped phases. We study the twist defects for a variety of bosonic ADE fractional quantum spin Hall systems for which the anyonic symmetries turn out to be given by their Dynkin diagrams. We also look at superconducting heterostructures with fermionic quantum Hall states and show the presence of anyonic symmetries and twist defects which physically correspond to a fermion parity flip. This can result in Majorana bound states at such defects instead of more exotic parafermions as was believed before. This is because the presence of the superconductor necessitates the consideration of a larger bosonic topological order. We then investigate the twist defects further by promoting the anyonic symmetries from global to local. This deconfines the defects and results in non-Abelian topological states called twist liquids. Finally, we study the emergence of new topological order from two constituent systems driven by the condensation of a composite boson. This allows us to study a variety of systems with non-Abelian excitations.","abstract_has_math":false,"creators":["Khan, Mayukh Nilay"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Hughes, Taylor L.","Stone, Michael","Eckstein, James N.","Peng, Jen-Chieh"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2018,"date_issued":"2018-03-13T15:45:06Z","date_published":"2018-03-13T15:45:06Z","updated_at":"2026-07-22T22:24:37Z","subjects":["twist defects","anyonic symmetry","anyon condensation","parafermions","non-Abelian bound states."],"languages":["en"],"rights":["Copyright 2017 Mayukh Nilay Khan"],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/2142/99304","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Hughes, Taylor L.","Stone, Michael","Eckstein, James N.","Peng, Jen-Chieh"]},{"key":"dc:creator","label":"Author","values":["Khan, Mayukh Nilay"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2018-03-13T15:45:06Z","2017-10-13","2017-12"]},{"key":"dc:type","label":"Dc Type","values":["text"]},{"key":"thesis:degree_discipline","label":"Discipline","values":["Physics"]},{"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":["twist defects","anyonic symmetry","anyon condensation","parafermions","non-Abelian bound states."]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["en"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 2017 Mayukh Nilay Khan"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["http://hdl.handle.net/2142/99304"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["Non-Abelian excitations are sought after because of the promise they hold for topological quantum computation. However, in spite of many proposals of systems in which they can occur intrinsically, observation has proved to be elusive. In this thesis, we study ways in which we can engineer such excitations by combining two parent Abelian theories, and as a result allow for defects which host non-Abelian zero modes. We first formulate the symmetries of the anyonic excitations of Abelian topological states. Then, we study properties of semiclassical point defects, called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. Non-Abelian twist defects appear between different gapped phases. We study the twist defects for a variety of bosonic ADE fractional quantum spin Hall systems for which the anyonic symmetries turn out to be given by their Dynkin diagrams. We also look at superconducting heterostructures with fermionic quantum Hall states and show the presence of anyonic symmetries and twist defects which physically correspond to a fermion parity flip. This can result in Majorana bound states at such defects instead of more exotic parafermions as was believed before. This is because the presence of the superconductor necessitates the consideration of a larger bosonic topological order. We then investigate the twist defects further by promoting the anyonic symmetries from global to local. This deconfines the defects and results in non-Abelian topological states called twist liquids. Finally, we study the emergence of new topological order from two constituent systems driven by the condensation of a composite boson. This allows us to study a variety of systems with non-Abelian excitations.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Mayukh Khan, accepted the attached license on 2017-10-11 at 14:37.","The student, Mayukh Khan, submitted this Dissertation for approval on 2017-10-11 at 14:44.","This Dissertation was approved for publication on 2017-10-13 at 09:34.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11680 on 2018-03-13 at 10:07:55","Made available in DSpace on 2018-03-13T15:45:06Z (GMT). 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In this thesis, we study ways in which we can engineer such excitations by combining two parent Abelian theories, and as a result allow for defects which host non-Abelian zero modes. We first formulate the symmetries of the anyonic excitations of Abelian topological states. Then, we study properties of semiclassical point defects, called twist defects, which permute orbiting anyons by their symmetries. We see how to realize these defects at domain walls on the gapped edges of non-chiral fractional quantum Hall states. We have distinct gapped edge phases in one to one correspondence with the anyonic symmetries. Non-Abelian twist defects appear between different gapped phases. We study the twist defects for a variety of bosonic ADE fractional quantum spin Hall systems for which the anyonic symmetries turn out to be given by their Dynkin diagrams. We also look at superconducting heterostructures with fermionic quantum Hall states and show the presence of anyonic symmetries and twist defects which physically correspond to a fermion parity flip. This can result in Majorana bound states at such defects instead of more exotic parafermions as was believed before. This is because the presence of the superconductor necessitates the consideration of a larger bosonic topological order. We then investigate the twist defects further by promoting the anyonic symmetries from global to local. This deconfines the defects and results in non-Abelian topological states called twist liquids. Finally, we study the emergence of new topological order from two constituent systems driven by the condensation of a composite boson. This allows us to study a variety of systems with non-Abelian excitations.","Submission original under an indefinite embargo labeled 'Open Access'. The submission was exported from vireo on 2018-03-13 without embargo terms","The student, Mayukh Khan, accepted the attached license on 2017-10-11 at 14:37.","The student, Mayukh Khan, submitted this Dissertation for approval on 2017-10-11 at 14:44.","This Dissertation was approved for publication on 2017-10-13 at 09:34.","DSpace SAF Submission Ingestion Package generated from Vireo submission #11680 on 2018-03-13 at 10:07:55","Made available in DSpace on 2018-03-13T15:45:06Z (GMT). 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