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Properties of Thermal Quantum States: Locality of Temperature, Decay of Correlations, and More

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Thermodynamics in the Quantum Regime

Part of the book series: Fundamental Theories of Physics ((FTPH,volume 195))

Abstract

We review several properties of thermal states of spin Hamiltonians with short range interactions. In particular, we focus on those aspects in which the application of tools coming from quantum information theory has been specially successful in the recent years. This comprises the study of the correlations at finite and zero temperature, the stability against distant and/or weak perturbations, the locality of temperature and their classical simulatability. For the case of states with a finite correlation length, we review the results on their energy distribution and the equivalence of the canonical and microcanonical ensemble.

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Notes

  1. 1.

    The discrepancy of the factor of 2 in the inverse temperature bound is due to considering two copies of the system in the proof of Theorem 1.

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Acknowledgements

We would like to thank C. Gogolin for helpful comments. The work of MK was funded by the National Science Centre, Poland within the project Polonez (2015/19/P/ST2/ 03001) which has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement No 665778. AR acknowledges Generalitat de Catalunya (AGAUR Grant No. 2017 SGR 1341, SGR 875 and CERCA/Program), the Spanish Ministry MINECO (National Plan 15 Grant:FISICATEAMO No. FIS2016-79508-P, SEVERO OCHOA No. SEV-2015-0522), Fundació Cellex, ERC AdG OSYRIS, EU FETPRO QUIC, and the CELLEX-ICFO-MPQ fellowship.

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Authors and Affiliations

  1. Institute of Theoretical Physics and Astrophysics, National Quantum Information Centre, University of Gdańsk, ul. Gen. Wl. Andersa 27, 81-824, Sopot, Poland

    Martin Kliesch

  2. Institute for Theoretical Physics, Heinrich Heine University Düsseldorf, Universitätsstraße 1, 40225, Düsseldorf, Germany

    Martin Kliesch

  3. ICFO – Institut de Ciencies Fotoniques, The Barcelona Institute of Science and Technology, 08860, Castelldefels, Spain

    Arnau Riera

  4. Max-Planck-Institut für Quantenoptik, 85748, Garching, Germany

    Arnau Riera

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  1. Martin Kliesch
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Correspondence to Martin Kliesch .

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Editors and Affiliations

  1. School of Physical and Mathematical Sciences, Nanyang Technological University, Singapore, Singapore

    Felix Binder

  2. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Luis A. Correa

  3. ICFO: Institut de Ciencies Fotoniques, Barcelona Institute of Science and Technology, Castelldefels, Spain

    Christian Gogolin

  4. CEMPS, Physics and Astronomy, University of Exeter, Exeter, UK

    Janet Anders

  5. School of Mathematical Sciences, University of Nottingham, Nottingham, UK

    Gerardo Adesso

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Kliesch, M., Riera, A. (2018). Properties of Thermal Quantum States: Locality of Temperature, Decay of Correlations, and More. In: Binder, F., Correa, L., Gogolin, C., Anders, J., Adesso, G. (eds) Thermodynamics in the Quantum Regime. Fundamental Theories of Physics, vol 195. Springer, Cham. https://doi.org/10.1007/978-3-319-99046-0_20

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