{"id":{"repo_id":"uiuc","oai_identifier":"oai:www.ideals.illinois.edu:2142/22005"},"canonical_url":"https://search.dev.ndltd.org/etd/uiuc/oai:www.ideals.illinois.edu:2142/22005","repository":{"repo_id":"uiuc","name":"University of Illinois - Urbana-Champaign","base_url":"https://www.ideals.illinois.edu/oai-pmh"},"display":{"title":"Dual mappings and phase transitions in a short-range random valence bond theory","abstract":"This thesis describes calculations done in 3-D Short-Range Random Valence Bond theory. After reviewing the background of SRRVB and how it can be derived, I cover the technique of dual mappings, with a particular emphasis on the Compact U(1) model, the monopole loop gas picture, and the confinement/deconfinement phase transition. The argument is then made that an equivalent phase transition may exist in the 3-D SRRVB, based on its mapping onto a similar monopole loop gas picture, albeit complicated by the presence of Berry phases. Building on results from the 2-D model, I also argue for the existence of a second phase transition; this being the melting from a Valence-Bond Crystal to a Quantum Spin Liquid. To demonstrate the existence of one or both of these phase transitions, I have proformed numerical simulations using Monte Carlo. The confinement/deconfinement phase transition is tracked using both hysteresis and Wilson loop measurements, starting from the Compact U(1) model and slowly modifying the background and the anisotropy. The VBC/QSL phase transition is investigated by direct modeling of the J-V version of the SRRVB and measuring various correlation functions.","abstract_html":"This thesis describes calculations done in 3-D Short-Range Random Valence Bond theory. After reviewing the background of SRRVB and how it can be derived, I cover the technique of dual mappings, with a particular emphasis on the Compact U(1) model, the monopole loop gas picture, and the confinement/deconfinement phase transition. The argument is then made that an equivalent phase transition may exist in the 3-D SRRVB, based on its mapping onto a similar monopole loop gas picture, albeit complicated by the presence of Berry phases. Building on results from the 2-D model, I also argue for the existence of a second phase transition; this being the melting from a Valence-Bond Crystal to a Quantum Spin Liquid. To demonstrate the existence of one or both of these phase transitions, I have proformed numerical simulations using Monte Carlo. The confinement/deconfinement phase transition is tracked using both hysteresis and Wilson loop measurements, starting from the Compact U(1) model and slowly modifying the background and the anisotropy. The VBC/QSL phase transition is investigated by direct modeling of the J-V version of the SRRVB and measuring various correlation functions.","abstract_has_math":false,"creators":["Sienko, Tanya Christine"],"institution":"University of Illinois at Urbana-Champaign","degree_name":"Ph.D.","degree_level":"Dissertation","degree_discipline":"Physics","degree_department":null,"school":null,"contributors":["Kogut, John B."],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2011,"date_issued":"2011-05-07T13:25:54Z","date_published":"2011-05-07T13:25:54Z","updated_at":"2026-07-22T22:25:19Z","subjects":["Physics, Condensed Matter","Physics, Elementary Particles and High Energy"],"languages":["eng"],"rights":["Copyright 1995 Sienko, Tanya Christine"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543722","(UMI)AAI9543722"],"render_values":[{"text":"AAI9543722","href":null,"code":true},{"text":"(UMI)AAI9543722","href":null,"code":true}]}]},"links":{"outbound_url":"http://hdl.handle.net/2142/22005","outbound_label":"Handle","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Kogut, John B."]},{"key":"dc:creator","label":"Author","values":["Sienko, Tanya Christine"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date","label":"Dc Date","values":["2011-05-07T13:25:54Z","10000-01-01","1995"]},{"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":["Physics, Condensed Matter","Physics, Elementary Particles and High Energy"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["eng"]},{"key":"dc:rights","label":"Dc Rights","values":["Copyright 1995 Sienko, Tanya Christine"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["AAI9543722","(UMI)AAI9543722","http://hdl.handle.net/2142/22005"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["This thesis describes calculations done in 3-D Short-Range Random Valence Bond theory. After reviewing the background of SRRVB and how it can be derived, I cover the technique of dual mappings, with a particular emphasis on the Compact U(1) model, the monopole loop gas picture, and the confinement/deconfinement phase transition. The argument is then made that an equivalent phase transition may exist in the 3-D SRRVB, based on its mapping onto a similar monopole loop gas picture, albeit complicated by the presence of Berry phases. Building on results from the 2-D model, I also argue for the existence of a second phase transition; this being the melting from a Valence-Bond Crystal to a Quantum Spin Liquid. To demonstrate the existence of one or both of these phase transitions, I have proformed numerical simulations using Monte Carlo. The confinement/deconfinement phase transition is tracked using both hysteresis and Wilson loop measurements, starting from the Compact U(1) model and slowly modifying the background and the anisotropy. The VBC/QSL phase transition is investigated by direct modeling of the J-V version of the SRRVB and measuring various correlation functions.","Made available in DSpace on 2011-05-07T13:25:54Z (GMT). No. of bitstreams: 2 license.txt: 4922 bytes, checksum: 910b249b4beec47e7ab768910c8f966f (MD5) 9543722.pdf: 2819929 bytes, checksum: 56fab144666e096c79ceb1fbcbfaa364 (MD5) Previous issue date: 1995","Item marked as restricted to the 'UIUC Users [automated]' Group (id=2) by Howard Ding (hding2@illinois.edu) on 2011-05-07T14:54:41Z Item is restricted indefinitely.","Restriction data tranferred 2014-07-01T11:25:26-05:00 Original Data Group with Access UIUC Users [automated] Release Date: none Reason: ETDs are only available to UIUC Users without author permission","ETDs are only available to UIUC Users without author permission","U of I Only"]},{"key":"dc:title","label":"Title","values":["Dual mappings and phase transitions in a short-range random valence bond theory"]}]}],"canonical_facts":{"dc:contributor":["Kogut, John B."],"dc:creator":["Sienko, Tanya Christine"],"dc:date":["2011-05-07T13:25:54Z","10000-01-01","1995"],"dc:description":["This thesis describes calculations done in 3-D Short-Range Random Valence Bond theory. After reviewing the background of SRRVB and how it can be derived, I cover the technique of dual mappings, with a particular emphasis on the Compact U(1) model, the monopole loop gas picture, and the confinement/deconfinement phase transition. The argument is then made that an equivalent phase transition may exist in the 3-D SRRVB, based on its mapping onto a similar monopole loop gas picture, albeit complicated by the presence of Berry phases. Building on results from the 2-D model, I also argue for the existence of a second phase transition; this being the melting from a Valence-Bond Crystal to a Quantum Spin Liquid. To demonstrate the existence of one or both of these phase transitions, I have proformed numerical simulations using Monte Carlo. The confinement/deconfinement phase transition is tracked using both hysteresis and Wilson loop measurements, starting from the Compact U(1) model and slowly modifying the background and the anisotropy. 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