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dc.creatorSanz-Vicario J.L.spa
dc.creatorPérez-Torres J.F.spa
dc.creatorMoreno-Polo G.spa
dc.date.accessioned2017-12-19T19:36:43Z
dc.date.available2017-12-19T19:36:43Z
dc.date.created2017
dc.identifier.issn24699926
dc.identifier.urihttp://hdl.handle.net/11407/4272
dc.description.abstractWe compute the entanglement between the electronic and vibrational motions in the simplest molecular system, the hydrogen molecular ion, considering the molecule as a bipartite system, electron and vibrational motion. For that purpose we compute an accurate total non-Born-Oppenheimer wave function in terms of a huge expansion using nonorthogonal B-spline basis sets that expand separately the electronic and nuclear wave functions. According to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, it is possible to find a much shorter but equivalent expansion in terms of the natural orbitals or Schmidt bases for the electronic and nuclear half spaces. Here we extend the Schmidt decomposition theorem to the case in which nonorthogonal bases are used to span the partitioned Hilbert spaces. This extension is first illustrated with two simple coupled systems, the former without an exact solution and the latter exactly solvable. In these model systems of distinguishable coupled particles it is shown that the entanglement content does not increase monotonically with the excitation energy, but only within the manifold of states that belong to an existing excitation mode, if any. In the hydrogen molecular ion the entanglement content for each non-Born-Oppenheimer vibronic state is quantified through the von Neumann and linear entropies and we show that entanglement serves as a witness to distinguish vibronic states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes. © 2017 American Physical Society.eng
dc.language.isoeng
dc.publisherAmerican Physical Societyspa
dc.relation.isversionofhttps://www.scopus.com/inward/record.uri?eid=2-s2.0-85028652124&doi=10.1103%2fPhysRevA.96.022503&partnerID=40&md5=f167f8f2d91e906abf6c02ab6b2bc1b0spa
dc.sourceScopusspa
dc.titleElectronic-nuclear entanglement in H2+: Schmidt decomposition of non-Born-Oppenheimer wave functions expanded in nonorthogonal basis setsspa
dc.typeArticleeng
dc.rights.accessrightsinfo:eu-repo/semantics/restrictedAccess
dc.contributor.affiliationSanz-Vicario, J.L., Grupo de Física Atómica y Molecular, Instituto de Física, Universidad de Antioquia, Medellín, Colombiaspa
dc.contributor.affiliationPérez-Torres, J.F., Facultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombia, Escuela de Química, Universidad Industrial de Santander, Bucaramanga, Colombiaspa
dc.contributor.affiliationMoreno-Polo, G., Grupo de Física Atómica y Molecular, Instituto de Física, Universidad de Antioquia, Medellín, Colombiaspa
dc.identifier.doi10.1103/PhysRevA.96.022503
dc.subject.keywordDomain decomposition methodseng
dc.subject.keywordExcited stateseng
dc.subject.keywordGeometryeng
dc.subject.keywordInformation theoryeng
dc.subject.keywordIon sourceseng
dc.subject.keywordQuantum opticseng
dc.subject.keywordQuantum theoryeng
dc.subject.keywordWave functionseng
dc.subject.keywordElectronic excitationeng
dc.subject.keywordHydrogen molecular ioneng
dc.subject.keywordNon-Born Oppenheimereng
dc.subject.keywordNonorthogonal basiseng
dc.subject.keywordNuclear wave functionseng
dc.subject.keywordQuantum information theoryeng
dc.subject.keywordSchmidt decompositioneng
dc.subject.keywordVibrational motionseng
dc.subject.keywordQuantum entanglementeng
dc.publisher.facultyFacultad de Ciencias Básicasspa
dc.abstractWe compute the entanglement between the electronic and vibrational motions in the simplest molecular system, the hydrogen molecular ion, considering the molecule as a bipartite system, electron and vibrational motion. For that purpose we compute an accurate total non-Born-Oppenheimer wave function in terms of a huge expansion using nonorthogonal B-spline basis sets that expand separately the electronic and nuclear wave functions. According to the Schmidt decomposition theorem for bipartite systems, widely used in quantum-information theory, it is possible to find a much shorter but equivalent expansion in terms of the natural orbitals or Schmidt bases for the electronic and nuclear half spaces. Here we extend the Schmidt decomposition theorem to the case in which nonorthogonal bases are used to span the partitioned Hilbert spaces. This extension is first illustrated with two simple coupled systems, the former without an exact solution and the latter exactly solvable. In these model systems of distinguishable coupled particles it is shown that the entanglement content does not increase monotonically with the excitation energy, but only within the manifold of states that belong to an existing excitation mode, if any. In the hydrogen molecular ion the entanglement content for each non-Born-Oppenheimer vibronic state is quantified through the von Neumann and linear entropies and we show that entanglement serves as a witness to distinguish vibronic states related to different Born-Oppenheimer molecular energy curves or electronic excitation modes. © 2017 American Physical Society.eng
dc.creator.affiliationGrupo de Física Atómica y Molecular, Instituto de Física, Universidad de Antioquia, Medellín, Colombiaspa
dc.creator.affiliationFacultad de Facultad de Ciencias Básicas, Universidad de Medellín, Medellín, Colombiaspa
dc.creator.affiliationEscuela de Química, Universidad Industrial de Santander, Bucaramanga, Colombiaspa
dc.relation.ispartofesPhysical Review Aspa
dc.relation.ispartofesPhysical Review A Volume 96, Issue 2, 2 August 2017spa
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dc.type.versioninfo:eu-repo/semantics/publishedVersion
dc.type.driverinfo:eu-repo/semantics/article
dc.identifier.reponamereponame:Repositorio Institucional Universidad de Medellínspa
dc.identifier.instnameinstname:Universidad de Medellínspa


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