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Spatial decay of Kubo’s canonical correlation functions

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Abstract

Kubo’s canonical correlation functions (canonical correlators) describe the static response of a system in equilibrium to infinitesimal local perturbations. Knowing their decay properties with respect to spatial distance is important for many theoretical and experimental applications. For a thermal state of a system with short-range interactions, we prove that any knowledge of the decay rate of ordinary correlators readily translates into that of canonical correlators. As the former have been extensively studied, our result can lead to many new results on the latter. Throughout the paper, we use the framework of infinite-volume quantum lattice model. However, the method we use is adaptable for other physical scenarios not considered in this paper.

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Notes

  1. KMS stands for Kubo–Martin–Schwinger.

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Acknowledgements

I would like to express my gratitude toward Anton Kapustin for suggesting the problem and for his invaluable guidance and support. I also thank Nathaniel Sagman, Tamir Hemo and Alexandre Perozim de Faveri for discussions on decay rates.

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  1. California Institute of Technology, Pasadena, CA, 91125, USA

    Bowen Yang

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  1. Bowen Yang
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Correspondence to Bowen Yang.

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Yang, B. Spatial decay of Kubo’s canonical correlation functions. Lett Math Phys 111, 97 (2021). https://doi.org/10.1007/s11005-021-01441-x

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  • DOI: https://doi.org/10.1007/s11005-021-01441-x

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