Manifestations of Dynamical Localization in the Disordered XXZ Spin Chain

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Abstract

We study disordered XXZ spin chains in the Ising phase exhibiting droplet localization, a single cluster localization property we previously proved for random XXZ spin chains. It holds in an energy interval I near the bottom of the spectrum, known as the droplet spectrum. We establish dynamical manifestations of localization in the energy window I, including non-spreading of information, zero-velocity Lieb–Robinson bounds, and general dynamical clustering. Our results do not rely on knowledge of the dynamical characteristics of the model outside the droplet spectrum. A byproduct of our analysis is that for random XXZ spin chains this droplet localization can happen only inside the droplet spectrum.

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© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of MathematicsVirginia TechBlacksburgUSA
  2. 2.Department of MathematicsUniversity of California, IrvineIrvineUSA
  3. 3.Department of MathematicsUniversity of Alabama at BirminghamBirminghamUSA

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