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Low-Energy Fock-Space Localization for Attractive Hard-Core Particles in Disorder

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Abstract

We study a one-dimensional quantum system with an arbitrary number of hard-core particles on the lattice, which are subject to a deterministic attractive interaction as well as a random potential. Our choice of interaction is suggested by the spectral analysis of the XXZ quantum spin chain. The main result concerns a version of high-disorder Fock-space localization expressed here in the configuration space of hard-core particles. The proof relies on an energetically motivated Combes–Thomas estimate and an effective one-particle analysis. As an application, we show the exponential decay of the two-point function in the infinite system uniformly in the particle number.

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Acknowledgements

We thank B. Nachtergaele for proposing the problem and for illuminating discussions during his stay at TUM as a John von Neumann Fellow. We are indebted to the referee for valuable comments. V.B. was supported by grant P2EZP2_162235 of the Swiss National Science Foundation.

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Authors and Affiliations

  1. Zentrum Mathematik, Technische Universität München, Boltzmannstr. 3, 85748, Garching bei München, Germany

    Vincent Beaud & Simone Warzel

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  1. Vincent Beaud
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  2. Simone Warzel
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Correspondence to Vincent Beaud.

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Communicated by Vieri Mastropietro.

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Beaud, V., Warzel, S. Low-Energy Fock-Space Localization for Attractive Hard-Core Particles in Disorder. Ann. Henri Poincaré 18, 3143–3166 (2017). https://doi.org/10.1007/s00023-017-0591-0

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  • DOI: https://doi.org/10.1007/s00023-017-0591-0

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