{"id":{"repo_id":"aachen","oai_identifier":"oai:publications.rwth-aachen.de:62951"},"canonical_url":"https://search.dev.ndltd.org/etd/aachen/oai:publications.rwth-aachen.de:62951","repository":{"repo_id":"aachen","name":"RWTH Aachen University","base_url":"https://publications.rwth-aachen.de/oai2d"},"display":{"title":"Grundzustandseigenschaften von anisotropen antiferromagnetischen Heisenberg-Ketten mit Spin S = 1","abstract":"In this thesis ground state properties of S = 1 spin chains with exchange and single-ion anisotropy are analysed. Following earlier publications two cases are mainly considered: A fixed ratio of the two anisotropies as well as a fixed and strong exchange anisotropy. The method primarily employed is the density matrix renormalization group (DMRG) for a finite chain length and in the thermodynamic limit (iDMRG). The phase diagrams of the quantum spin chain and the corresponding classical model are compared for the first time. Thereby the similarity of the phase diagrams, the correspondence of the phases and the striking differences are elucidated. The various phases of the quantum model include antiferromagnetic, ferromagnetic, spin liquid and supersolid phases. Their properties are discussed in detail. Analysing the correlation functions and using a correspondence to Luttinger liquids one can distinguish commensurate and incommensurate regions of the spin liquid phase. For different parameters the spin liquid phase may be subdivided into regions of ferroquadrupolar and spin-density-wave ordering. Some of the quantum phase transitions between the various phases are studied. Particularly the transition between the spin liquid and the supersolid phase is identified to be in the two-dimensional Ising universality class.","abstract_html":"In this thesis ground state properties of S = 1 spin chains with exchange and single-ion anisotropy are analysed. Following earlier publications two cases are mainly considered: A fixed ratio of the two anisotropies as well as a fixed and strong exchange anisotropy. The method primarily employed is the density matrix renormalization group (DMRG) for a finite chain length and in the thermodynamic limit (iDMRG). The phase diagrams of the quantum spin chain and the corresponding classical model are compared for the first time. Thereby the similarity of the phase diagrams, the correspondence of the phases and the striking differences are elucidated. The various phases of the quantum model include antiferromagnetic, ferromagnetic, spin liquid and supersolid phases. Their properties are discussed in detail. Analysing the correlation functions and using a correspondence to Luttinger liquids one can distinguish commensurate and incommensurate regions of the spin liquid phase. For different parameters the spin liquid phase may be subdivided into regions of ferroquadrupolar and spin-density-wave ordering. Some of the quantum phase transitions between the various phases are studied. Particularly the transition between the spin liquid and the supersolid phase is identified to be in the two-dimensional Ising universality class.","abstract_has_math":false,"creators":["Peters, David"],"institution":"Publikationsserver der RWTH Aachen University","degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":null,"school":null,"contributors":["Selke, Walter"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2012,"date_issued":"2012","date_published":"2012","updated_at":"2026-07-30T19:43:35Z","subjects":["info:eu-repo/classification/ddc/530","Vielteilchentheorie","Magnetismus","Festkörpertheorie","Luttinger-Flüssigkeit","Statistische Physik","Heisenberg-Modell","Quantenphasenübergang","Physik","Quantenmagnetismus","Quantenphasenübergänge","statistical physics","quantum magnetism","Heisenberg model","quantum phase transitions"],"languages":["ger"],"rights":["info:eu-repo/semantics/openAccess"],"rights_urls":[],"identifier_entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124424%22"],"render_values":[{"text":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124424%22","href":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124424%22","code":true}]}]},"links":{"outbound_url":"https://publications.rwth-aachen.de/record/62951","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Selke, Walter"]},{"key":"dc:creator","label":"Author","values":["Peters, David"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:coverage","label":"Dc Coverage","values":["DE"]},{"key":"dc:date","label":"Dc Date","values":["2012"]},{"key":"dc:publisher","label":"Institution","values":["Publikationsserver der RWTH Aachen University"]},{"key":"dc:relation","label":"Dc Relation","values":["info:eu-repo/semantics/altIdentifier/urn/urn:nbn:de:hbz:82-opus-39941"]},{"key":"dc:type","label":"Dc Type","values":["info:eu-repo/semantics/doctoralThesis","info:eu-repo/semantics/publishedVersion"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["info:eu-repo/classification/ddc/530","Vielteilchentheorie","Magnetismus","Festkörpertheorie","Luttinger-Flüssigkeit","Statistische Physik","Heisenberg-Modell","Quantenphasenübergang","Physik","Quantenmagnetismus","Quantenphasenübergänge","statistical physics","quantum magnetism","Heisenberg model","quantum phase transitions"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language","label":"Dc Language","values":["ger"]},{"key":"dc:rights","label":"Dc Rights","values":["info:eu-repo/semantics/openAccess"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://publications.rwth-aachen.de/record/62951","https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-124424%22"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description","label":"Description","values":["In this thesis ground state properties of S = 1 spin chains with exchange and single-ion anisotropy are analysed. Following earlier publications two cases are mainly considered: A fixed ratio of the two anisotropies as well as a fixed and strong exchange anisotropy. The method primarily employed is the density matrix renormalization group (DMRG) for a finite chain length and in the thermodynamic limit (iDMRG). The phase diagrams of the quantum spin chain and the corresponding classical model are compared for the first time. Thereby the similarity of the phase diagrams, the correspondence of the phases and the striking differences are elucidated. The various phases of the quantum model include antiferromagnetic, ferromagnetic, spin liquid and supersolid phases. Their properties are discussed in detail. Analysing the correlation functions and using a correspondence to Luttinger liquids one can distinguish commensurate and incommensurate regions of the spin liquid phase. For different parameters the spin liquid phase may be subdivided into regions of ferroquadrupolar and spin-density-wave ordering. Some of the quantum phase transitions between the various phases are studied. Particularly the transition between the spin liquid and the supersolid phase is identified to be in the two-dimensional Ising universality class."]},{"key":"dc:source","label":"Dc Source","values":["Aachen : Publikationsserver der RWTH Aachen University 96 S. : graph. Darst. (2012). = Aachen, Techn. Hochsch., Diss., 2012"]},{"key":"dc:title","label":"Title","values":["Grundzustandseigenschaften von anisotropen antiferromagnetischen Heisenberg-Ketten mit Spin S = 1"]}]}],"canonical_facts":{"dc:contributor":["Selke, Walter"],"dc:coverage":["DE"],"dc:creator":["Peters, David"],"dc:date":["2012"],"dc:description":["In this thesis ground state properties of S = 1 spin chains with exchange and single-ion anisotropy are analysed. Following earlier publications two cases are mainly considered: A fixed ratio of the two anisotropies as well as a fixed and strong exchange anisotropy. 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