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Locality Estimates for Complex Time Evolution in 1D

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dc.contributor.authorPérez García, David
dc.contributor.authorPérez Hernández, Antonio
dc.contributor.funderAgencia Estatal de Investigación
dc.contributor.funderComunidad de Madrid
dc.date.accessioned2026-02-20T11:59:43Z
dc.date.available2026-02-20T11:59:43Z
dc.date.issued2023-01-03
dc.descriptionThe registered version of this article, first published in “Commun. Math. Phys. 399, 2023", is available online at the publisher's website: Springer, https://doi.org/10.1007/s00220-022-04573-w
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en “Commun. Math. Phys. 399, 2023", está disponible en línea en el sitio web del editor: Springer, https://doi.org/10.1007/s00220-022-04573-w
dc.description.abstractIt is a generalized belief that there are no thermal phase transitions in short range 1D quantum systems. However, the only known case for which this is rigorously proven is for the particular case of finite range translationally invariant interactions. The proof was obtained by Araki in his seminal paper of 1969 as a consequence of pioneering locality estimates for the time-evolution operator that allowed him to prove its analyticity on the whole complex plane, whenappliedtoalocalobservable. However, as for nowthere is no mathematical proof of the absence of 1D thermal phase transitions if one allows exponential tails in the interactions. In this work we extend Araki’s result to include exponential (or faster) tails. Our main result is the analyticity of the timeevolution operator applied on a local observable on a suitable strip around the real line. As a consequence we obtain that thermal states in 1D exhibit exponential decay of correlations above a threshold temperature that decays to zero with the exponent of the interaction decay, recovering Araki’s result as a particular case. Our result however still leaves open the possibility of 1D thermal short range phase transitions. We conclude with an application of our result to the spectral gap problem for Projected Entangled Pair States (PEPS) on 2D lattices, via the holographic duality due to Cirac et al.en
dc.description.provenanceMade available in DSpace on 2026-02-20T11:59:43Z (GMT). No. of bitstreams: 1 Perez_Hernandez_Antonio_Locality_estimates_1D_ANTONIO PEREZ HERNAN.pdf: 642992 bytes, checksum: ca9cf0416a423bcdaf18bb07a2f62a65 (MD5) Previous issue date: 2023-01-03en
dc.description.versionversión publicada
dc.identifier.citationPérez-García, D., Pérez-Hernández, A. Locality Estimates for Complex Time Evolution in 1D. Commun. Math. Phys. 399, 929–970 (2023). https://doi.org/10.1007/s00220-022-04573-w
dc.identifier.doihttps://doi.org/10.1007/s00220-022-04573-w
dc.identifier.eissn1432-0916
dc.identifier.issn0010-3616
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31874
dc.journal.titleCommunications in Mathematical Physics
dc.journal.volume399
dc.language.isoen
dc.page.final970
dc.page.initial929
dc.publisherSpringer
dc.relation.centerEscuela Técnica Superior de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.relation.projectidinfo:eu-repo/grantAgreement/UE/ERC/GAPS (N. 648913)/Spectral gaps in interacting quantum systems
dc.relation.projectidinfo:eu-repo/grantAgreement/MINECO//SEV-2015-0554
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI/Programa Estatal de Fomento de la Investigación Científica y Técnica de Excelencia, 2017/MTM2017-88385-P /Modelización matemática y simulación numérica de problemas en ciencias e ingeniería: aplicaciones industriales y medioambientales
dc.relation.projectidinfo:eu-repo/grantAgreement/MICIN/Plan Estatal de Investigación Científica y Técnica y de Innovación 2017-2020/PID2020-113523GB-I00/Análisis Matemático y Teoría de la Información Cuántica
dc.relation.projectidinfo:eu-repo/grantAgreement/S2018/TCS-4342/QUITEMAD-CM
dc.relation.projectidinfo:eu-repo/grantAgreement/AEI//FJC2018-036519-I
dc.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.titleLocality Estimates for Complex Time Evolution in 1Den
dc.typeartículoes
dc.typejournal articleen
dspace.entity.typePublication
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relation.isAuthorOfPublication.latestForDiscovery5df1117e-e057-404a-a139-4d4aab6e5298
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