{"id":{"repo_id":"mcmaster","oai_identifier":"oai:macsphere.mcmaster.ca:11375/28877"},"canonical_url":"https://search.dev.ndltd.org/etd/mcmaster/oai:macsphere.mcmaster.ca:11375/28877","repository":{"repo_id":"mcmaster","name":"McMaster University","base_url":"https://macsphere.mcmaster.ca/server/oai/request"},"display":{"title":"On the Phase Diagram of the Heisenberg Gamma Ladder","abstract":"Quantum spin liquids (QSLs) may roughly be defined as states possessing sufficiently high quantum fluctuations that they impede long range magnetic order. Various electron interactions are currently being studied in order to physically realize such states in condensed matter systems since they can host fractionalized excitations. The purpose of our study is to examine two interactions established as important in the literature while not having been paired together. We consider a bond-dependant $J$-$\\Gamma$ ladder, comprised of an alternating symmetric exchange of spin components, mediated by $\\Gamma$, along with a Heisenberg interaction controlled by $J$. By parameterizing these couplings by an angle $\\phi$, we produce a phase diagram of the system using the Infinite Density Matrix Renormalization Group (iDMRG) numerical technique. In order to classify the phases, we search for discontinuities in the entanglement spectrum for bonds along one of the legs and the rungs of the ladder while also looking at divergences in the susceptibility of the energy. These criteria reveal a possible 10 phases hosted by the system, with 7 of them showing some form of magnetic ordering seen directly from the spin correlations and by applying magnetic fields in appropriate directions. Moreover, known points in the phase diagram can be adiabatically connected to other points within the same phase by tuning $J$ or $\\Gamma$. The remaining three phases however show no obvious long-range magnetic order while also having large contributions to the entanglement spectrum. Such phases, showing interesting initial signs, are discussed further in our study.","abstract_html":"Quantum spin liquids (QSLs) may roughly be defined as states possessing sufficiently high quantum fluctuations that they impede long range magnetic order. Various electron interactions are currently being studied in order to physically realize such states in condensed matter systems since they can host fractionalized excitations. The purpose of our study is to examine two interactions established as important in the literature while not having been paired together. We consider a bond-dependant $J$-$\\Gamma$ ladder, comprised of an alternating symmetric exchange of spin components, mediated by $\\Gamma$, along with a Heisenberg interaction controlled by $J$. By parameterizing these couplings by an angle $\\phi$, we produce a phase diagram of the system using the Infinite Density Matrix Renormalization Group (iDMRG) numerical technique. In order to classify the phases, we search for discontinuities in the entanglement spectrum for bonds along one of the legs and the rungs of the ladder while also looking at divergences in the susceptibility of the energy. These criteria reveal a possible 10 phases hosted by the system, with 7 of them showing some form of magnetic ordering seen directly from the spin correlations and by applying magnetic fields in appropriate directions. Moreover, known points in the phase diagram can be adiabatically connected to other points within the same phase by tuning $J$ or $\\Gamma$. The remaining three phases however show no obvious long-range magnetic order while also having large contributions to the entanglement spectrum. Such phases, showing interesting initial signs, are discussed further in our study.","abstract_has_math":true,"creators":["Avakian, Sébastien"],"institution":null,"degree_name":null,"degree_level":null,"degree_discipline":null,"degree_department":"Physics and Astronomy","school":null,"contributors":[],"advisors":["Sorensen, Erik"],"committee_chairs":[],"committee_members":[],"year":2023,"date_issued":"2023","date_published":"2023","updated_at":"2026-08-21T16:46:30Z","subjects":["Condensed Matter Physics","DMRG","Spin Chains","SPT phases"],"languages":["en"],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"http://hdl.handle.net/11375/28877","outbound_label":"Handle","outbound_source":"dc:identifier.uri"},"source_record":{"url":"https://macsphere.mcmaster.ca/server/oai/request?verb=GetRecord&metadataPrefix=dim&identifier=oai%3Amacsphere.mcmaster.ca%3A11375%2F28877","prefix":"dim"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor.advisor","label":"Advisor","values":["Sorensen, Erik"]},{"key":"dc:contributor.department","label":"Department","values":["Physics and Astronomy"]},{"key":"dc:creator","label":"Author","values":["Avakian, Sébastien"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"dc:date.accessioned","label":"Dc Date Accessioned","values":["2023-09-08T14:43:18Z"]},{"key":"dc:date.available","label":"Dc Date Available","values":["2023-09-08T14:43:18Z"]},{"key":"dc:date.issued","label":"Date","values":["2023"]},{"key":"dc:type","label":"Dc Type","values":["Thesis"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Condensed Matter Physics","DMRG","Spin Chains","SPT phases"]}]},{"id":"language_rights","label":"Language and Rights","entries":[{"key":"dc:language.iso","label":"Language (ISO)","values":["en"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier.uri","label":"Identifier URI","values":["http://hdl.handle.net/11375/28877"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["Quantum spin liquids (QSLs) may roughly be defined as states possessing sufficiently high quantum fluctuations that they impede long range magnetic order. Various electron interactions are currently being studied in order to physically realize such states in condensed matter systems since they can host fractionalized excitations. The purpose of our study is to examine two interactions established as important in the literature while not having been paired together. We consider a bond-dependant $J$-$\\Gamma$ ladder, comprised of an alternating symmetric exchange of spin components, mediated by $\\Gamma$, along with a Heisenberg interaction controlled by $J$. By parameterizing these couplings by an angle $\\phi$, we produce a phase diagram of the system using the Infinite Density Matrix Renormalization Group (iDMRG) numerical technique. In order to classify the phases, we search for discontinuities in the entanglement spectrum for bonds along one of the legs and the rungs of the ladder while also looking at divergences in the susceptibility of the energy. These criteria reveal a possible 10 phases hosted by the system, with 7 of them showing some form of magnetic ordering seen directly from the spin correlations and by applying magnetic fields in appropriate directions. Moreover, known points in the phase diagram can be adiabatically connected to other points within the same phase by tuning $J$ or $\\Gamma$. The remaining three phases however show no obvious long-range magnetic order while also having large contributions to the entanglement spectrum. Such phases, showing interesting initial signs, are discussed further in our study."]},{"key":"dc:description.degree","label":"Dc Description Degree","values":["Master of Science (MSc)"]},{"key":"dc:title","label":"Title","values":["On the Phase Diagram of the Heisenberg Gamma Ladder"]}]}],"canonical_facts":{"dc:contributor.advisor":["Sorensen, Erik"],"dc:contributor.department":["Physics and Astronomy"],"dc:creator":["Avakian, Sébastien"],"dc:date.accessioned":["2023-09-08T14:43:18Z"],"dc:date.available":["2023-09-08T14:43:18Z"],"dc:date.issued":["2023"],"dc:description.abstract":["Quantum spin liquids (QSLs) may roughly be defined as states possessing sufficiently high quantum fluctuations that they impede long range magnetic order. Various electron interactions are currently being studied in order to physically realize such states in condensed matter systems since they can host fractionalized excitations. The purpose of our study is to examine two interactions established as important in the literature while not having been paired together. We consider a bond-dependant $J$-$\\Gamma$ ladder, comprised of an alternating symmetric exchange of spin components, mediated by $\\Gamma$, along with a Heisenberg interaction controlled by $J$. By parameterizing these couplings by an angle $\\phi$, we produce a phase diagram of the system using the Infinite Density Matrix Renormalization Group (iDMRG) numerical technique. In order to classify the phases, we search for discontinuities in the entanglement spectrum for bonds along one of the legs and the rungs of the ladder while also looking at divergences in the susceptibility of the energy. These criteria reveal a possible 10 phases hosted by the system, with 7 of them showing some form of magnetic ordering seen directly from the spin correlations and by applying magnetic fields in appropriate directions. Moreover, known points in the phase diagram can be adiabatically connected to other points within the same phase by tuning $J$ or $\\Gamma$. The remaining three phases however show no obvious long-range magnetic order while also having large contributions to the entanglement spectrum. Such phases, showing interesting initial signs, are discussed further in our study."],"dc:description.degree":["Master of Science (MSc)"],"dc:identifier.uri":["http://hdl.handle.net/11375/28877"],"dc:language.iso":["en"],"dc:subject":["Condensed Matter Physics","DMRG","Spin Chains","SPT phases"],"dc:title":["On the Phase Diagram of the Heisenberg Gamma Ladder"],"dc:type":["Thesis"]},"updated_at":"2026-08-21T16:46:30Z"}