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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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Correspondence to Abel Klein.

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Communicated by L. Erdos

A.K. was supported in part by the NSF under Grant DMS-1301641. A.E. was supported in part by the Simons Foundation under grant #522404.

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Elgart, A., Klein, A. & Stolz, G. Manifestations of Dynamical Localization in the Disordered XXZ Spin Chain. Commun. Math. Phys. 361, 1083–1113 (2018). https://doi.org/10.1007/s00220-018-3132-x

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  • DOI: https://doi.org/10.1007/s00220-018-3132-x

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