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It is therefore of great interest to know when such states allow for an easy description. In particular, this is the case if correlations between distant regions are small. In this work, we consider 1D quantum spin systems with local, finite-range, translation-invariant interactions at any temperature. In this setting, we show that Gibbs states satisfy uniform exponential decay of correlations and, moreover, the mutual information between two regions decays exponentially with their distance, irrespective of the temperature. In order to prove the latter, we show that exponential decay of correlations of the infinite-chain thermal states, exponential uniform clustering and exponential decay of the mutual information are equivalent for 1D quantum spin systems with local, finite-range interactions at any temperature. In particular, Araki&amp;apos;s seminal results yields that the three conditions hold in the translation-invariant case. The methods we use are based on the Belavkin-Staszewski relative entropy and on techniques developed by Araki. Moreover, we find that the Gibbs states of the systems we consider are superexponentially close to saturating the data-processing inequality for the Belavkin-Staszewski relative entropy.<\/jats:p>","DOI":"10.22331\/q-2022-02-10-650","type":"journal-article","created":{"date-parts":[[2022,2,10]],"date-time":"2022-02-10T13:21:51Z","timestamp":1644499311000},"page":"650","update-policy":"https:\/\/doi.org\/10.22331\/q-crossmark-policy-page","source":"Crossref","is-referenced-by-count":30,"title":["Exponential decay of mutual information for Gibbs states of local Hamiltonians"],"prefix":"10.22331","volume":"6","author":[{"ORCID":"https:\/\/orcid.org\/0000-0003-4796-7633","authenticated-orcid":false,"given":"Andreas","family":"Bluhm","sequence":"first","affiliation":[{"name":"QMATH, Department of Mathematical Sciences, University of Copenhagen, Universitetsparken 5, 2100 Copenhagen, Denmark"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-6713-6760","authenticated-orcid":false,"given":"\u00c1ngela","family":"Capel","sequence":"additional","affiliation":[{"name":"Fachbereich Mathematik, Universit\u00e4t T\u00fcbingen, 72076 T\u00fcbingen, Germany"},{"name":"Zentrum Mathematik, Technische Universit\u00e4t M\u00fcnchen, Boltzmannstrasse 3, 85748 Garching, Germany"},{"name":"Munich Center for Quantum Science and Technology (MCQST), M\u00fcnchen, Germany"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-8600-7083","authenticated-orcid":false,"given":"Antonio","family":"P\u00e9rez-Hern\u00e1ndez","sequence":"additional","affiliation":[{"name":"Departamento de Matem\u00e1tica Aplicada I, Escuela T\u00e9cnica Superior de Ingenieros Industriales, Universidad Nacional de Educaci\u00f3n a Distancia, calle Juan del Rosal 12, 28040 Madrid (Ciudad Universitaria), Spain"},{"name":"Departamento de An\u00e1lisis Matem\u00e1tico y Matem\u00e1tica Aplicada, Universidad Complutense de Madrid, 28040 Madrid, Spain"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"9598","published-online":{"date-parts":[[2022,2,10]]},"reference":[{"key":"0","doi-asserted-by":"publisher","unstructured":"Y. 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