Detecting dimensional crossover and finite Hilbert space through entanglement entropies

Autores
Garagiola, Mariano; Cuestas, María Eloisa; Pont, Federico Manuel; Serra, Pablo; Osenda, Omar
Año de publicación
2016
Idioma
inglés
Tipo de recurso
artículo
Estado
versión publicada
Descripción
The information content of the two-particle one- and two-dimensional Calogero model is studied by using the von Neumann and Rényi entropies. The one-dimensional model is shown to have nonmonotonic entropies with finite values in the large-interaction-strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we show that the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated by using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The Rényi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a nonmonotonic and nonanalytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, the spectrum of the reduced density matrix are both finite.
Fil: Garagiola, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Cuestas, María Eloisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Pont, Federico Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Serra, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Osenda, Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Materia
Entanglement Entropies
Calogero Model
Harmonic Approximation
Nivel de accesibilidad
acceso abierto
Condiciones de uso
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repositorio
CONICET Digital (CONICET)
Institución
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identificador
oai:ri.conicet.gov.ar:11336/72458
Acceder
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spelling Detecting dimensional crossover and finite Hilbert space through entanglement entropiesGaragiola, MarianoCuestas, María EloisaPont, Federico ManuelSerra, PabloOsenda, OmarEntanglement EntropiesCalogero ModelHarmonic Approximationhttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The information content of the two-particle one- and two-dimensional Calogero model is studied by using the von Neumann and Rényi entropies. The one-dimensional model is shown to have nonmonotonic entropies with finite values in the large-interaction-strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we show that the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated by using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The Rényi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a nonmonotonic and nonanalytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, the spectrum of the reduced density matrix are both finite.Fil: Garagiola, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Cuestas, María Eloisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Pont, Federico Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Serra, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaFil: Osenda, Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; ArgentinaAmerican Physical Society2016-10info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/72458Garagiola, Mariano; Cuestas, María Eloisa; Pont, Federico Manuel; Serra, Pablo; Osenda, Omar; Detecting dimensional crossover and finite Hilbert space through entanglement entropies; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 94; 10-2016; 1-11; 0421151050-2947CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.94.042115info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.042115info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2025-09-03T10:08:07Zoai:ri.conicet.gov.ar:11336/72458instacron:CONICETInstitucionalhttp://ri.conicet.gov.ar/Organismo científico-tecnológicoNo correspondehttp://ri.conicet.gov.ar/oai/requestdasensio@conicet.gov.ar; lcarlino@conicet.gov.arArgentinaNo correspondeNo correspondeNo correspondeopendoar:34982025-09-03 10:08:08.03CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Detecting dimensional crossover and finite Hilbert space through entanglement entropies
title Detecting dimensional crossover and finite Hilbert space through entanglement entropies
spellingShingle Detecting dimensional crossover and finite Hilbert space through entanglement entropies
Garagiola, Mariano
Entanglement Entropies
Calogero Model
Harmonic Approximation
title_short Detecting dimensional crossover and finite Hilbert space through entanglement entropies
title_full Detecting dimensional crossover and finite Hilbert space through entanglement entropies
title_fullStr Detecting dimensional crossover and finite Hilbert space through entanglement entropies
title_full_unstemmed Detecting dimensional crossover and finite Hilbert space through entanglement entropies
title_sort Detecting dimensional crossover and finite Hilbert space through entanglement entropies
dc.creator.none.fl_str_mv Garagiola, Mariano
Cuestas, María Eloisa
Pont, Federico Manuel
Serra, Pablo
Osenda, Omar
author Garagiola, Mariano
author_facet Garagiola, Mariano
Cuestas, María Eloisa
Pont, Federico Manuel
Serra, Pablo
Osenda, Omar
author_role author
author2 Cuestas, María Eloisa
Pont, Federico Manuel
Serra, Pablo
Osenda, Omar
author2_role author
author
author
author
dc.subject.none.fl_str_mv Entanglement Entropies
Calogero Model
Harmonic Approximation
topic Entanglement Entropies
Calogero Model
Harmonic Approximation
purl_subject.fl_str_mv https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
dc.description.none.fl_txt_mv The information content of the two-particle one- and two-dimensional Calogero model is studied by using the von Neumann and Rényi entropies. The one-dimensional model is shown to have nonmonotonic entropies with finite values in the large-interaction-strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we show that the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated by using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The Rényi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a nonmonotonic and nonanalytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, the spectrum of the reduced density matrix are both finite.
Fil: Garagiola, Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Cuestas, María Eloisa. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Pont, Federico Manuel. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Serra, Pablo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
Fil: Osenda, Omar. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - Córdoba. Instituto de Física Enrique Gaviola. Universidad Nacional de Córdoba. Instituto de Física Enrique Gaviola; Argentina
description The information content of the two-particle one- and two-dimensional Calogero model is studied by using the von Neumann and Rényi entropies. The one-dimensional model is shown to have nonmonotonic entropies with finite values in the large-interaction-strength limit. On the other hand, the von Neumann entropy of the two-dimensional model with isotropic confinement is a monotone increasing function of the interaction strength which diverges logarithmically. By considering an anisotropic confinement in the two-dimensional case we show that the one-dimensional behavior is eventually reached when the anisotropy increases. The crossover from two to one dimensions is demonstrated by using the harmonic approximation and it is shown that the von Neumann divergence only occurs in the isotropic case. The Rényi entropies are used to highlight the structure of the model spectrum. In particular, it is shown that these entropies have a nonmonotonic and nonanalytical behavior in the neighborhood of the interaction strength parameter values where the Hilbert space and, consequently, the spectrum of the reduced density matrix are both finite.
publishDate 2016
dc.date.none.fl_str_mv 2016-10
dc.type.none.fl_str_mv info:eu-repo/semantics/article
info:eu-repo/semantics/publishedVersion
http://purl.org/coar/resource_type/c_6501
info:ar-repo/semantics/articulo
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/11336/72458
Garagiola, Mariano; Cuestas, María Eloisa; Pont, Federico Manuel; Serra, Pablo; Osenda, Omar; Detecting dimensional crossover and finite Hilbert space through entanglement entropies; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 94; 10-2016; 1-11; 042115
1050-2947
CONICET Digital
CONICET
url http://hdl.handle.net/11336/72458
identifier_str_mv Garagiola, Mariano; Cuestas, María Eloisa; Pont, Federico Manuel; Serra, Pablo; Osenda, Omar; Detecting dimensional crossover and finite Hilbert space through entanglement entropies; American Physical Society; Physical Review A: Atomic, Molecular and Optical Physics; 94; 10-2016; 1-11; 042115
1050-2947
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevA.94.042115
info:eu-repo/semantics/altIdentifier/url/https://journals.aps.org/pra/abstract/10.1103/PhysRevA.94.042115
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
eu_rights_str_mv openAccess
rights_invalid_str_mv https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
dc.format.none.fl_str_mv application/pdf
application/pdf
application/pdf
application/pdf
dc.publisher.none.fl_str_mv American Physical Society
publisher.none.fl_str_mv American Physical Society
dc.source.none.fl_str_mv reponame:CONICET Digital (CONICET)
instname:Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
repository.name.fl_str_mv CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicas
repository.mail.fl_str_mv dasensio@conicet.gov.ar; lcarlino@conicet.gov.ar
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score 13.13397

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