Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model

The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We...

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Autores: Wald, Sascha, Arias, Raúl Eduardo, Alba, Vincenzo
Formato: artículo
Estado:Versión publicada
Fecha de publicación:2020
País:Argentina
Recursos:Consejo Nacional de Investigaciones Científicas y Técnicas
Repositorio:CONICET Digital (CONICET)
Idioma:inglés
OAI Identifier:oai:ri.conicet.gov.ar:11336/145397
Acesso em linha:http://hdl.handle.net/11336/145397
Access Level:acceso abierto
Palavra-chave:ENTANGLEMENT SPECTRUM
QUANTUM ENTANGLEMENT
QUANTUM PHASE TRANSITIONS
QUANTUM STATISTICAL MECHANICS
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
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spelling Closure of the entanglement gap at quantum criticality: The case of the quantum spherical modelWald, SaschaArias, Raúl EduardoAlba, VincenzoENTANGLEMENT SPECTRUMQUANTUM ENTANGLEMENTQUANTUM PHASE TRANSITIONSQUANTUM STATISTICAL MECHANICShttps://purl.org/becyt/ford/1.3https://purl.org/becyt/ford/1The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as π2/ ln(L), with L the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap δξ ln(L) exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a nontrivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.Fil: Wald, Sascha. Max-planck-institut Für Physik Komplexer Systeme; AlemaniaFil: Arias, Raúl Eduardo. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata. Instituto de Física La Plata. Universidad Nacional de La Plata. Facultad de Ciencias Exactas. Instituto de Física La Plata; Argentina. Scuola Internazionale Superiore di Studi Avanzati; ItaliaFil: Alba, Vincenzo. University of Amsterdam; Países BajosAmerican Physical Society2020-12info:eu-repo/semantics/articleinfo:eu-repo/semantics/publishedVersionhttp://purl.org/coar/resource_type/c_6501info:ar-repo/semantics/articuloapplication/pdfapplication/pdfhttp://hdl.handle.net/11336/145397Wald, Sascha; Arias, Raúl Eduardo; Alba, Vincenzo; Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model; American Physical Society; Physical Review Research; 2; 043404; 12-2020; 1-192643-15642643-1564CONICET DigitalCONICETenginfo:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevResearch.2.043404info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevResearch.2.043404info:eu-repo/semantics/openAccesshttps://creativecommons.org/licenses/by-nc-sa/2.5/ar/reponame:CONICET Digital (CONICET)instname:Consejo Nacional de Investigaciones Científicas y Técnicas2024-05-08T13:44:51Zoai:ri.conicet.gov.ar:11336/145397instacron: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:34982024-05-08 13:44:52.114CONICET Digital (CONICET) - Consejo Nacional de Investigaciones Científicas y Técnicasfalse
dc.title.none.fl_str_mv Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
title Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
spellingShingle Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
Wald, Sascha
ENTANGLEMENT SPECTRUM
QUANTUM ENTANGLEMENT
QUANTUM PHASE TRANSITIONS
QUANTUM STATISTICAL MECHANICS
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
title_short Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
title_full Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
title_fullStr Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
title_full_unstemmed Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
title_sort Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
dc.creator.none.fl_str_mv Wald, Sascha
Arias, Raúl Eduardo
Alba, Vincenzo
author Wald, Sascha
author_facet Wald, Sascha
Arias, Raúl Eduardo
Alba, Vincenzo
author_role author
author2 Arias, Raúl Eduardo
Alba, Vincenzo
author2_role author
author
dc.subject.none.fl_str_mv ENTANGLEMENT SPECTRUM
QUANTUM ENTANGLEMENT
QUANTUM PHASE TRANSITIONS
QUANTUM STATISTICAL MECHANICS
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
topic ENTANGLEMENT SPECTRUM
QUANTUM ENTANGLEMENT
QUANTUM PHASE TRANSITIONS
QUANTUM STATISTICAL MECHANICS
https://purl.org/becyt/ford/1.3
https://purl.org/becyt/ford/1
description The study of entanglement spectra is a powerful tool to detect or elucidate universal behavior in quantum many-body systems. We investigate the scaling of the entanglement (or Schmidt) gap δξ , i.e., the lowest-laying gap of the entanglement spectrum, at a two-dimensional quantum critical point. We focus on the paradigmatic quantum spherical model, which exhibits a second-order transition and is mappable to free bosons with an additional external constraint. We analytically show that the Schmidt gap vanishes at the critical point, although only logarithmically. For a system on a torus and the half-system bipartition, the entanglement gap vanishes as π2/ ln(L), with L the linear system size. The entanglement gap is nonzero in the paramagnetic phase and exhibits a faster decay in the ordered phase. The rescaled gap δξ ln(L) exhibits a crossing for different system sizes at the transition, although logarithmic corrections prevent a precise verification of the finite-size scaling. Interestingly, the change of the entanglement gap across the phase diagram is reflected in the zero-mode eigenvector of the spin-spin correlator. At the transition quantum fluctuations give rise to a nontrivial structure of the eigenvector, whereas in the ordered phase it is flat. We also show that the vanishing of the entanglement gap at criticality can be qualitatively but not quantitatively captured by neglecting the structure of the zero-mode eigenvector.
publishDate 2020
dc.date.none.fl_str_mv 2020-12
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/11336/145397
Wald, Sascha; Arias, Raúl Eduardo; Alba, Vincenzo; Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model; American Physical Society; Physical Review Research; 2; 043404; 12-2020; 1-19
2643-1564
2643-1564
CONICET Digital
CONICET
url http://hdl.handle.net/11336/145397
identifier_str_mv Wald, Sascha; Arias, Raúl Eduardo; Alba, Vincenzo; Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model; American Physical Society; Physical Review Research; 2; 043404; 12-2020; 1-19
2643-1564
CONICET Digital
CONICET
dc.language.none.fl_str_mv eng
language eng
dc.relation.none.fl_str_mv info:eu-repo/semantics/altIdentifier/url/https://link.aps.org/doi/10.1103/PhysRevResearch.2.043404
info:eu-repo/semantics/altIdentifier/doi/10.1103/PhysRevResearch.2.043404
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
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
instname_str Consejo Nacional de Investigaciones Científicas y Técnicas
reponame_str CONICET Digital (CONICET)
collection CONICET Digital (CONICET)
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 15.812429

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