Closure of the entanglement gap at quantum criticality: The case of the quantum spherical model
- Autores
- Wald, Sascha; Arias, Raúl Eduardo; Alba, Vincenzo
- Año de publicación
- 2020
- Idioma
- inglés
- Tipo de recurso
- artículo
- Estado
- versión publicada
- Descripción
- 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.
Fil: Wald, Sascha. Max-planck-institut Für Physik Komplexer Systeme; Alemania
Fil: 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; Italia
Fil: Alba, Vincenzo. University of Amsterdam; Países Bajos - Materia
-
ENTANGLEMENT SPECTRUM
QUANTUM ENTANGLEMENT
QUANTUM PHASE TRANSITIONS
QUANTUM STATISTICAL MECHANICS - Nivel de accesibilidad
- acceso abierto
- Condiciones de uso
- https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
- Repositorio
- Institución
- Consejo Nacional de Investigaciones Científicas y Técnicas
- OAI Identificador
- oai:ri.conicet.gov.ar:11336/145397
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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 Técnicas2025-09-03T09:51:39Zoai: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:34982025-09-03 09:51:40.142CONICET 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 |
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 |
topic |
ENTANGLEMENT SPECTRUM QUANTUM ENTANGLEMENT QUANTUM PHASE TRANSITIONS QUANTUM STATISTICAL MECHANICS |
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 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; Alemania Fil: 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; Italia Fil: Alba, Vincenzo. University of Amsterdam; Países Bajos |
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 |
reponame_str |
CONICET Digital (CONICET) |
collection |
CONICET Digital (CONICET) |
instname_str |
Consejo Nacional de Investigaciones Científicas y Técnicas |
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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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