Locality of Temperature
This work is concerned with thermal quantum states of Hamiltonians on spin- and fermionic-lattice systems with short-range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of “intensivity of temperature” to interacting quantum models. More p...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
| Published: |
American Physical Society
2014-07-01
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| Series: | Physical Review X |
| Online Access: | http://doi.org/10.1103/PhysRevX.4.031019 |
| _version_ | 1819120691518111744 |
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| author | M. Kliesch C. Gogolin M. J. Kastoryano A. Riera J. Eisert |
| author_facet | M. Kliesch C. Gogolin M. J. Kastoryano A. Riera J. Eisert |
| author_sort | M. Kliesch |
| collection | DOAJ |
| description | This work is concerned with thermal quantum states of Hamiltonians on spin- and fermionic-lattice systems with short-range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of “intensivity of temperature” to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance, we prove exponential clustering of correlations above a universal critical temperature that upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature, local expectation values can be approximated efficiently in the error and the system size. |
| first_indexed | 2024-12-22T06:24:41Z |
| format | Article |
| id | doaj.art-bd7a957a95ac4db9ba41ecd58d906439 |
| institution | Directory Open Access Journal |
| issn | 2160-3308 |
| language | English |
| last_indexed | 2024-12-22T06:24:41Z |
| publishDate | 2014-07-01 |
| publisher | American Physical Society |
| record_format | Article |
| series | Physical Review X |
| spelling | doaj.art-bd7a957a95ac4db9ba41ecd58d9064392022-12-21T18:35:52ZengAmerican Physical SocietyPhysical Review X2160-33082014-07-014303101910.1103/PhysRevX.4.031019Locality of TemperatureM. KlieschC. GogolinM. J. KastoryanoA. RieraJ. EisertThis work is concerned with thermal quantum states of Hamiltonians on spin- and fermionic-lattice systems with short-range interactions. We provide results leading to a local definition of temperature, thereby extending the notion of “intensivity of temperature” to interacting quantum models. More precisely, we derive a perturbation formula for thermal states. The influence of the perturbation is exactly given in terms of a generalized covariance. For this covariance, we prove exponential clustering of correlations above a universal critical temperature that upper bounds physical critical temperatures such as the Curie temperature. As a corollary, we obtain that above the critical temperature, thermal states are stable against distant Hamiltonian perturbations. Moreover, our results imply that above the critical temperature, local expectation values can be approximated efficiently in the error and the system size.http://doi.org/10.1103/PhysRevX.4.031019 |
| spellingShingle | M. Kliesch C. Gogolin M. J. Kastoryano A. Riera J. Eisert Locality of Temperature Physical Review X |
| title | Locality of Temperature |
| title_full | Locality of Temperature |
| title_fullStr | Locality of Temperature |
| title_full_unstemmed | Locality of Temperature |
| title_short | Locality of Temperature |
| title_sort | locality of temperature |
| url | http://doi.org/10.1103/PhysRevX.4.031019 |
| work_keys_str_mv | AT mkliesch localityoftemperature AT cgogolin localityoftemperature AT mjkastoryano localityoftemperature AT ariera localityoftemperature AT jeisert localityoftemperature |