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Dynamical Localization in Disordered Quantum Spin Systems

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Abstract

We say that a quantum spin system is dynamically localized if the time-evolution of local observables satisfies a zero-velocity Lieb-Robinson bound. In terms of this definition we have the following main results: First, for general systems with short range interactions, dynamical localization implies exponential decay of ground state correlations, up to an explicit correction. Second, the dynamical localization of random xy spin chains can be reduced to dynamical localization of an effective one-particle Hamiltonian. In particular, the isotropic xy chain in random exterior magnetic field is dynamically localized.

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Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Science, Cairo University, Cairo, 12613, Egypt

    Eman Hamza

  2. Department of Mathematics, University of Arizona, Tucson, AZ, 85721, USA

    Robert Sims

  3. Department of Mathematics, University of Alabama at Birmingham, Birmingham, AL, 35294, USA

    Günter Stolz

Authors
  1. Eman Hamza
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  2. Robert Sims
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  3. Günter Stolz
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Corresponding author

Correspondence to Robert Sims.

Additional information

Communicated by H. Spohn

R. S. was supported in part by NSF grants DMS-0757424 and DMS-1101345.

G. S. was supported in part by NSF grants DMS-0653374 and DMS-1069320.

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Hamza, E., Sims, R. & Stolz, G. Dynamical Localization in Disordered Quantum Spin Systems. Commun. Math. Phys. 315, 215–239 (2012). https://doi.org/10.1007/s00220-012-1544-6

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