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Fecha
2022-02-10
Derechos de acceso
info:eu-repo/semantics/openAccess
Título de la revista
ISSN de la revista
Título del volumen
Editorial
Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften
Citas
Resumen
The thermal equilibrium properties of physical systems can be described using Gibbs states. 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'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.
Descripción
The registered version of this article, first published in “Quantum, 6, 2022", is available online at the publisher's website: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, https://doi.org/10.22331/q-2022-02-10-650
La versión registrada de este artículo, publicado por primera vez en “Quantum, 6, 2022", está disponible en línea en el sitio web del editor: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, https://doi.org/10.22331/q-2022-02-10-650
La versión registrada de este artículo, publicado por primera vez en “Quantum, 6, 2022", está disponible en línea en el sitio web del editor: Verein zur Förderung des Open Access Publizierens in den Quantenwissenschaften, https://doi.org/10.22331/q-2022-02-10-650
Categorías UNESCO
Palabras clave
Citación
Andreas Bluhm, Ángela Capel, Antonio Pérez-Hernández (2022). Exponential decay of mutual information for Gibbs states of local Hamiltonians. Quantum, 6, 650. DOI: 10.22331/q-2022-02-10-650
Centro
Escuela Técnica Superior de Ingenieros Industriales
Departamento
Matemática Aplicada I