Entropic Order Parameters for Categorical Symmetries in 2D-CFT

In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (Formula presented.) -d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs re...

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Detalles Bibliográficos
Autores: Molina-Vilaplana, J., Saura-Bastida, P., Sierra, G.
Tipo de recurso: artículo
Estado:Versión publicada
Fecha de publicación:2024
País:España
Institución:Consejo Superior de Investigaciones Científicas (CSIC)
Repositorio:DIGITAL.CSIC. Repositorio Institucional del CSIC
OAI Identifier:oai:digital.csic.es:10261/381902
Acceso en línea:http://hdl.handle.net/10261/381902
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85213403933&doi=10.3390%2fe26121064&partnerID=40&md5=11a27e7c1b83dd06d657cc1da40438c9
Access Level:acceso abierto
Palabra clave:Categorical symmetries
Conformal field theory
Relative entropy
Symmetry breaking
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spelling Entropic Order Parameters for Categorical Symmetries in 2D-CFTMolina-Vilaplana, J.Saura-Bastida, P.Sierra, G.Categorical symmetriesConformal field theoryRelative entropySymmetry breakingIn this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (Formula presented.) -d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (Formula presented.) -d theories with categorical symmetries. © 2024 by the authors.The work of P.S.-B. is supported by Fundación Séneca de la Región de Murcia, grant 21609/FPI/21. J.M.-V. thanks the financial support of Spanish Ministerio de Ciencia e Innovación PID2021-125700NAC22. G.S. acknowledges financial support through the Spanish MINECO grant PID2021-127726NB-I00, the CSIC Research Platform on Quantum Technologies PTI-001 and the QUANTUM ENIA project Quantum Spain through the RTRP-Next Generation within the framework of the Digital Spain 2026 Agenda.Peer reviewedMultidisciplinary Digital Publishing InstituteMinisterio de Ciencia e Innovación (España)Fundación SénecaAgencia Estatal de Investigación (España)Ministerio de de Economía, Comercio y Empresa (España)Consejo Superior de Investigaciones Científicas (España)European CommissionConsejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]202520252024info:eu-repo/semantics/articlehttp://purl.org/coar/resource_type/c_6501Publisher's versioninfo:eu-repo/semantics/publishedVersionapplication/pdfhttp://hdl.handle.net/10261/381902https://www.scopus.com/inward/record.uri?eid=2-s2.0-85213403933&doi=10.3390%2fe26121064&partnerID=40&md5=11a27e7c1b83dd06d657cc1da40438c9reponame:DIGITAL.CSIC. Repositorio Institucional del CSICinstname:Consejo Superior de Investigaciones Científicas (CSIC)Inglés#PLACEHOLDER_PARENT_METADATA_VALUE##PLACEHOLDER_PARENT_METADATA_VALUE#info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-125700NA-C22info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-127726NB-I00https://doi.org/10.3390/e26121064Síinfo:eu-repo/semantics/openAccessoai:digital.csic.es:10261/3819022026-05-22T06:33:51Z
dc.title.none.fl_str_mv Entropic Order Parameters for Categorical Symmetries in 2D-CFT
title Entropic Order Parameters for Categorical Symmetries in 2D-CFT
spellingShingle Entropic Order Parameters for Categorical Symmetries in 2D-CFT
Molina-Vilaplana, J.
Categorical symmetries
Conformal field theory
Relative entropy
Symmetry breaking
title_short Entropic Order Parameters for Categorical Symmetries in 2D-CFT
title_full Entropic Order Parameters for Categorical Symmetries in 2D-CFT
title_fullStr Entropic Order Parameters for Categorical Symmetries in 2D-CFT
title_full_unstemmed Entropic Order Parameters for Categorical Symmetries in 2D-CFT
title_sort Entropic Order Parameters for Categorical Symmetries in 2D-CFT
dc.creator.none.fl_str_mv Molina-Vilaplana, J.
Saura-Bastida, P.
Sierra, G.
author Molina-Vilaplana, J.
author_facet Molina-Vilaplana, J.
Saura-Bastida, P.
Sierra, G.
author_role author
author2 Saura-Bastida, P.
Sierra, G.
author2_role author
author
dc.contributor.none.fl_str_mv Ministerio de Ciencia e Innovación (España)
Fundación Séneca
Agencia Estatal de Investigación (España)
Ministerio de de Economía, Comercio y Empresa (España)
Consejo Superior de Investigaciones Científicas (España)
European Commission
Consejo Superior de Investigaciones Científicas [https://ror.org/02gfc7t72]
dc.subject.none.fl_str_mv Categorical symmetries
Conformal field theory
Relative entropy
Symmetry breaking
topic Categorical symmetries
Conformal field theory
Relative entropy
Symmetry breaking
description In this work, we propose an information theoretic order parameter able to characterize the presence and breaking of categorical symmetries in (Formula presented.) -d rational conformal field theories (RCFTs). Specifically, we compute the quantum relative entropy between the ground states of RCFTs representing the critical point of phase transitions between different symmetry-broken phases of theories with categorical symmetries, and their symmetrized versions. We find that, at leading order in the high temperature limit, this relative entropy only depends on the expectation values of the quantum dimensions of the topological operators implementing the categorical symmetry. This dependence suggests that our proposal can be used to characterize the different broken phases of (Formula presented.) -d theories with categorical symmetries. © 2024 by the authors.
publishDate 2024
dc.date.none.fl_str_mv 2024
2025
2025
dc.type.none.fl_str_mv info:eu-repo/semantics/article
http://purl.org/coar/resource_type/c_6501
Publisher's version
info:eu-repo/semantics/publishedVersion
format article
status_str publishedVersion
dc.identifier.none.fl_str_mv http://hdl.handle.net/10261/381902
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85213403933&doi=10.3390%2fe26121064&partnerID=40&md5=11a27e7c1b83dd06d657cc1da40438c9
url http://hdl.handle.net/10261/381902
https://www.scopus.com/inward/record.uri?eid=2-s2.0-85213403933&doi=10.3390%2fe26121064&partnerID=40&md5=11a27e7c1b83dd06d657cc1da40438c9
dc.language.none.fl_str_mv Inglés
language_invalid_str_mv Inglés
dc.relation.none.fl_str_mv #PLACEHOLDER_PARENT_METADATA_VALUE#
#PLACEHOLDER_PARENT_METADATA_VALUE#
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-125700NA-C22
info:eu-repo/grantAgreement/AEI/Plan Estatal de Investigación Científica y Técnica y de Innovación 2021-2023/PID2021-127726NB-I00
https://doi.org/10.3390/e26121064
Sí
dc.rights.none.fl_str_mv info:eu-repo/semantics/openAccess
eu_rights_str_mv openAccess
dc.format.none.fl_str_mv application/pdf
dc.publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
publisher.none.fl_str_mv Multidisciplinary Digital Publishing Institute
dc.source.none.fl_str_mv reponame:DIGITAL.CSIC. Repositorio Institucional del CSIC
instname:Consejo Superior de Investigaciones Científicas (CSIC)
instname_str Consejo Superior de Investigaciones Científicas (CSIC)
reponame_str DIGITAL.CSIC. Repositorio Institucional del CSIC
collection DIGITAL.CSIC. Repositorio Institucional del CSIC
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