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Strong Decay of Correlations for Gibbs States in Any Dimension

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dc.contributor.authorBluhm, Andreas
dc.contributor.authorCapel, Ángela
dc.contributor.authorPérez Hernández, Antonio
dc.contributor.funderAgencia Estatal de Investigación
dc.contributor.funderComunidad de Madrid
dc.date.accessioned2026-02-20T13:18:00Z
dc.date.available2026-02-20T13:18:00Z
dc.date.issued2025-09-29
dc.descriptionThe registered version of this article, first published in “Journal of Statistical Physics, vol. 192, 2025", is available online at the publisher's website: Springer, https://doi.org/10.1007/s10955-025-03512-y
dc.descriptionLa versión registrada de este artículo, publicado por primera vez en “Journal of Statistical Physics, vol. 192, 2025", está disponible en línea en el sitio web del editor: Springer, https://doi.org/10.1007/s10955-025-03512-y
dc.description.abstractQuantum systems in thermal equilibrium are described using Gibbs states. The correlations in such states determine how difficult it is to describe or simulate them. In this article, we show that if the Gibbs state of a quantum system satisfies that each of its marginals admits a local effective Hamiltonian with short-range interactions, then it satisfies a mixing condition, that is, for any regions A, C the distance of the reduced state on these regions to the product of its marginals, ρACρ−1 A ⊗ρ−1 C −1AC , decays exponentially with the distance between regions A and C. This mixing condition is stronger than other commonly studied measures of correlation. In particular, it implies the exponential decay of the mutual information between distant regions. The mixing condition has been used, for example, to prove positive log-Sobolev constants. On the way, we prove that the the condition regarding local effective Hamiltonian is satisfied if the Hamiltonian only has commuting interactions which also commute with every marginal of their products. The proof of these results employs a variety of tools such as Araki’s expansionals, quantum belief propagation and cluster expansions.en
dc.description.provenanceMade available in DSpace on 2026-02-20T13:18:00Z (GMT). No. of bitstreams: 1 Perez_Hernandez_Antonio_Strong_Decay_Correlat_ANTONIO PEREZ HERNAN.pdf: 1847564 bytes, checksum: 32b6c873cf0cb34b5d8de1c2a8223e93 (MD5) Previous issue date: 2025-09-29en
dc.description.versionversión publicada
dc.identifier.citationBluhm, A., Capel, Á. & Pérez-Hernández, A. Strong Decay of Correlations for Gibbs States in Any Dimension. J Stat Phys 192, 134 (2025). https://doi.org/10.1007/s10955-025-03512-y
dc.identifier.doihttps://doi.org/10.1007/s10955-025-03512-y
dc.identifier.eissn1572-9613
dc.identifier.issn0022-4715
dc.identifier.urihttps://hdl.handle.net/20.500.14468/31881
dc.journal.issue134
dc.journal.titleJournal of Statistical Physics
dc.journal.volume192
dc.language.isoen
dc.publisherSpringer
dc.relation.centerEscuela Técnica Superior de Ingenieros Industriales
dc.relation.departmentMatemática Aplicada I
dc.relation.projectidinfo:eu-repo/grantAgreement/DFG/CRC 2023-2026/ID 470903074 – TRR 352/Mathematics of Many-Body Quantum Systems and Their Collective Phenomena
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.rightsinfo:eu-repo/semantics/openAccess
dc.rights.urihttp://creativecommons.org/licenses/by/4.0/deed.es
dc.subject12 Matemáticas
dc.titleStrong Decay of Correlations for Gibbs States in Any Dimensionen
dc.typeartículoes
dc.typejournal articleen
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relation.isAuthorOfPublication5df1117e-e057-404a-a139-4d4aab6e5298
relation.isAuthorOfPublication.latestForDiscovery5df1117e-e057-404a-a139-4d4aab6e5298
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