Entanglement oscillations near a quantum critical point
Autor(a) principal: | |
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Data de Publicação: | 2020 |
Outros Autores: | , , |
Tipo de documento: | Artigo |
Idioma: | eng |
Título da fonte: | Repositório Institucional da UFRN |
Texto Completo: | https://repositorio.ufrn.br/handle/123456789/30466 |
Resumo: | We study the dynamics of entanglement in the scaling limit of the Ising spin chain in the presence of both a longitudinal and a transverse field. We present analytical results for the quench of the longitudinal field in the critical transverse field which go beyond current lattice integrability techniques. We test these results against a numerical simulation on the corresponding lattice model finding extremely good agreement. We show that the presence of bound states in the spectrum of the field theory leads to oscillations in the entanglement entropy and suppresses its linear growth on the time scales accessible to numerical simulations. For small quenches, we exactly determine these oscillatory contributions and demonstrate that their presence follows from symmetry arguments. For the quench of the transverse field at zero longitudinal field, we prove that the R´ enyi entropies are exactly proportional to the logarithm of the exponential of a time-dependent function, whose leading large-time behavior is linear, hence, entanglement grows linearly. We conclude that, in the scaling limit, linear growth and oscillations in the entanglement entropies can not be simply seen as consequences of integrability and its breaking, respectively |
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Castro-Alvaredo, Olalla A.Lencsés, MátéSzécsényi, István M.Viti, Jacopo2020-10-20T23:51:26Z2020-10-20T23:51:26Z2020-06-11CASTRO-ALVAREDO, Olalla A.; LENCSÉS, Máté; SZÉCSÉNYI, István M.; VITI, Jacopo. Entanglement Oscillations near a Quantum Critical Point. Physical Review Letters, [S.L.], v. 124, n. 23, p. 1-7, 11 jun. 2020. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.230601. Acesso em 11 ago. 2020. http://dx.doi.org/10.1103/physrevlett.124.2306011079-7114https://repositorio.ufrn.br/handle/123456789/3046610.1103/PhysRevLett.124.230601American Physical SocietyEntanglement oscillationQuantum critical pointEntanglement oscillations near a quantum critical pointinfo:eu-repo/semantics/publishedVersioninfo:eu-repo/semantics/articleWe study the dynamics of entanglement in the scaling limit of the Ising spin chain in the presence of both a longitudinal and a transverse field. We present analytical results for the quench of the longitudinal field in the critical transverse field which go beyond current lattice integrability techniques. We test these results against a numerical simulation on the corresponding lattice model finding extremely good agreement. We show that the presence of bound states in the spectrum of the field theory leads to oscillations in the entanglement entropy and suppresses its linear growth on the time scales accessible to numerical simulations. For small quenches, we exactly determine these oscillatory contributions and demonstrate that their presence follows from symmetry arguments. For the quench of the transverse field at zero longitudinal field, we prove that the R´ enyi entropies are exactly proportional to the logarithm of the exponential of a time-dependent function, whose leading large-time behavior is linear, hence, entanglement grows linearly. We conclude that, in the scaling limit, linear growth and oscillations in the entanglement entropies can not be simply seen as consequences of integrability and its breaking, respectivelyengreponame:Repositório Institucional da UFRNinstname:Universidade Federal do Rio Grande do Norte (UFRN)instacron:UFRNinfo:eu-repo/semantics/openAccessORIGINALEntanglementOscillations_VITI_2020.pdfEntanglementOscillations_VITI_2020.pdfapplication/pdf421205https://repositorio.ufrn.br/bitstream/123456789/30466/1/EntanglementOscillations_VITI_2020.pdfeff414f28aff77af8d08e37102081516MD51LICENSElicense.txtlicense.txttext/plain; charset=utf-81484https://repositorio.ufrn.br/bitstream/123456789/30466/2/license.txte9597aa2854d128fd968be5edc8a28d9MD52TEXTEntanglementOscillations_VITI_2020.pdf.txtEntanglementOscillations_VITI_2020.pdf.txtExtracted texttext/plain35582https://repositorio.ufrn.br/bitstream/123456789/30466/3/EntanglementOscillations_VITI_2020.pdf.txt4b41d957b84d78d43ba6b0b380387134MD53THUMBNAILEntanglementOscillations_VITI_2020.pdf.jpgEntanglementOscillations_VITI_2020.pdf.jpgGenerated Thumbnailimage/jpeg1693https://repositorio.ufrn.br/bitstream/123456789/30466/4/EntanglementOscillations_VITI_2020.pdf.jpgd46708a04f159353845aea5b559d2170MD54123456789/304662020-10-25 04:56:06.242oai:https://repositorio.ufrn.br:123456789/30466Tk9OLUVYQ0xVU0lWRSBESVNUUklCVVRJT04gTElDRU5TRQoKCkJ5IHNpZ25pbmcgYW5kIGRlbGl2ZXJpbmcgdGhpcyBsaWNlbnNlLCBNci4gKGF1dGhvciBvciBjb3B5cmlnaHQgaG9sZGVyKToKCgphKSBHcmFudHMgdGhlIFVuaXZlcnNpZGFkZSBGZWRlcmFsIFJpbyBHcmFuZGUgZG8gTm9ydGUgdGhlIG5vbi1leGNsdXNpdmUgcmlnaHQgb2YKcmVwcm9kdWNlLCBjb252ZXJ0IChhcyBkZWZpbmVkIGJlbG93KSwgY29tbXVuaWNhdGUgYW5kIC8gb3IKZGlzdHJpYnV0ZSB0aGUgZGVsaXZlcmVkIGRvY3VtZW50IChpbmNsdWRpbmcgYWJzdHJhY3QgLyBhYnN0cmFjdCkgaW4KZGlnaXRhbCBvciBwcmludGVkIGZvcm1hdCBhbmQgaW4gYW55IG1lZGl1bS4KCmIpIERlY2xhcmVzIHRoYXQgdGhlIGRvY3VtZW50IHN1Ym1pdHRlZCBpcyBpdHMgb3JpZ2luYWwgd29yaywgYW5kIHRoYXQKeW91IGhhdmUgdGhlIHJpZ2h0IHRvIGdyYW50IHRoZSByaWdodHMgY29udGFpbmVkIGluIHRoaXMgbGljZW5zZS4gRGVjbGFyZXMKdGhhdCB0aGUgZGVsaXZlcnkgb2YgdGhlIGRvY3VtZW50IGRvZXMgbm90IGluZnJpbmdlLCBhcyBmYXIgYXMgaXQgaXMKdGhlIHJpZ2h0cyBvZiBhbnkgb3RoZXIgcGVyc29uIG9yIGVudGl0eS4KCmMpIElmIHRoZSBkb2N1bWVudCBkZWxpdmVyZWQgY29udGFpbnMgbWF0ZXJpYWwgd2hpY2ggZG9lcyBub3QKcmlnaHRzLCBkZWNsYXJlcyB0aGF0IGl0IGhhcyBvYnRhaW5lZCBhdXRob3JpemF0aW9uIGZyb20gdGhlIGhvbGRlciBvZiB0aGUKY29weXJpZ2h0IHRvIGdyYW50IHRoZSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gR3JhbmRlIGRvIE5vcnRlIHRoZSByaWdodHMgcmVxdWlyZWQgYnkgdGhpcyBsaWNlbnNlLCBhbmQgdGhhdCB0aGlzIG1hdGVyaWFsIHdob3NlIHJpZ2h0cyBhcmUgb2YKdGhpcmQgcGFydGllcyBpcyBjbGVhcmx5IGlkZW50aWZpZWQgYW5kIHJlY29nbml6ZWQgaW4gdGhlIHRleHQgb3IKY29udGVudCBvZiB0aGUgZG9jdW1lbnQgZGVsaXZlcmVkLgoKSWYgdGhlIGRvY3VtZW50IHN1Ym1pdHRlZCBpcyBiYXNlZCBvbiBmdW5kZWQgb3Igc3VwcG9ydGVkIHdvcmsKYnkgYW5vdGhlciBpbnN0aXR1dGlvbiBvdGhlciB0aGFuIHRoZSBVbml2ZXJzaWRhZGUgRmVkZXJhbCBkbyBSaW8gR3JhbmRlIGRvIE5vcnRlLCBkZWNsYXJlcyB0aGF0IGl0IGhhcyBmdWxmaWxsZWQgYW55IG9ibGlnYXRpb25zIHJlcXVpcmVkIGJ5IHRoZSByZXNwZWN0aXZlIGFncmVlbWVudCBvciBhZ3JlZW1lbnQuCgpUaGUgVW5pdmVyc2lkYWRlIEZlZGVyYWwgZG8gUmlvIEdyYW5kZSBkbyBOb3J0ZSB3aWxsIGNsZWFybHkgaWRlbnRpZnkgaXRzIG5hbWUgKHMpIGFzIHRoZSBhdXRob3IgKHMpIG9yIGhvbGRlciAocykgb2YgdGhlIGRvY3VtZW50J3MgcmlnaHRzCmRlbGl2ZXJlZCwgYW5kIHdpbGwgbm90IG1ha2UgYW55IGNoYW5nZXMsIG90aGVyIHRoYW4gdGhvc2UgcGVybWl0dGVkIGJ5CnRoaXMgbGljZW5zZQo=Repositório de PublicaçõesPUBhttp://repositorio.ufrn.br/oai/opendoar:2020-10-25T07:56:06Repositório Institucional da UFRN - Universidade Federal do Rio Grande do Norte (UFRN)false |
dc.title.pt_BR.fl_str_mv |
Entanglement oscillations near a quantum critical point |
title |
Entanglement oscillations near a quantum critical point |
spellingShingle |
Entanglement oscillations near a quantum critical point Castro-Alvaredo, Olalla A. Entanglement oscillation Quantum critical point |
title_short |
Entanglement oscillations near a quantum critical point |
title_full |
Entanglement oscillations near a quantum critical point |
title_fullStr |
Entanglement oscillations near a quantum critical point |
title_full_unstemmed |
Entanglement oscillations near a quantum critical point |
title_sort |
Entanglement oscillations near a quantum critical point |
author |
Castro-Alvaredo, Olalla A. |
author_facet |
Castro-Alvaredo, Olalla A. Lencsés, Máté Szécsényi, István M. Viti, Jacopo |
author_role |
author |
author2 |
Lencsés, Máté Szécsényi, István M. Viti, Jacopo |
author2_role |
author author author |
dc.contributor.author.fl_str_mv |
Castro-Alvaredo, Olalla A. Lencsés, Máté Szécsényi, István M. Viti, Jacopo |
dc.subject.por.fl_str_mv |
Entanglement oscillation Quantum critical point |
topic |
Entanglement oscillation Quantum critical point |
description |
We study the dynamics of entanglement in the scaling limit of the Ising spin chain in the presence of both a longitudinal and a transverse field. We present analytical results for the quench of the longitudinal field in the critical transverse field which go beyond current lattice integrability techniques. We test these results against a numerical simulation on the corresponding lattice model finding extremely good agreement. We show that the presence of bound states in the spectrum of the field theory leads to oscillations in the entanglement entropy and suppresses its linear growth on the time scales accessible to numerical simulations. For small quenches, we exactly determine these oscillatory contributions and demonstrate that their presence follows from symmetry arguments. For the quench of the transverse field at zero longitudinal field, we prove that the R´ enyi entropies are exactly proportional to the logarithm of the exponential of a time-dependent function, whose leading large-time behavior is linear, hence, entanglement grows linearly. We conclude that, in the scaling limit, linear growth and oscillations in the entanglement entropies can not be simply seen as consequences of integrability and its breaking, respectively |
publishDate |
2020 |
dc.date.accessioned.fl_str_mv |
2020-10-20T23:51:26Z |
dc.date.available.fl_str_mv |
2020-10-20T23:51:26Z |
dc.date.issued.fl_str_mv |
2020-06-11 |
dc.type.status.fl_str_mv |
info:eu-repo/semantics/publishedVersion |
dc.type.driver.fl_str_mv |
info:eu-repo/semantics/article |
format |
article |
status_str |
publishedVersion |
dc.identifier.citation.fl_str_mv |
CASTRO-ALVAREDO, Olalla A.; LENCSÉS, Máté; SZÉCSÉNYI, István M.; VITI, Jacopo. Entanglement Oscillations near a Quantum Critical Point. Physical Review Letters, [S.L.], v. 124, n. 23, p. 1-7, 11 jun. 2020. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.230601. Acesso em 11 ago. 2020. http://dx.doi.org/10.1103/physrevlett.124.230601 |
dc.identifier.uri.fl_str_mv |
https://repositorio.ufrn.br/handle/123456789/30466 |
dc.identifier.issn.none.fl_str_mv |
1079-7114 |
dc.identifier.doi.none.fl_str_mv |
10.1103/PhysRevLett.124.230601 |
identifier_str_mv |
CASTRO-ALVAREDO, Olalla A.; LENCSÉS, Máté; SZÉCSÉNYI, István M.; VITI, Jacopo. Entanglement Oscillations near a Quantum Critical Point. Physical Review Letters, [S.L.], v. 124, n. 23, p. 1-7, 11 jun. 2020. Disponível em: https://journals.aps.org/prl/abstract/10.1103/PhysRevLett.124.230601. Acesso em 11 ago. 2020. http://dx.doi.org/10.1103/physrevlett.124.230601 1079-7114 10.1103/PhysRevLett.124.230601 |
url |
https://repositorio.ufrn.br/handle/123456789/30466 |
dc.language.iso.fl_str_mv |
eng |
language |
eng |
dc.rights.driver.fl_str_mv |
info:eu-repo/semantics/openAccess |
eu_rights_str_mv |
openAccess |
dc.publisher.none.fl_str_mv |
American Physical Society |
publisher.none.fl_str_mv |
American Physical Society |
dc.source.none.fl_str_mv |
reponame:Repositório Institucional da UFRN instname:Universidade Federal do Rio Grande do Norte (UFRN) instacron:UFRN |
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