Manifestations of dynamical localization in the disordered XXZ spin chain

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.

32 pages, no figures

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Cited by in corpus (14)

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• Power law logarithmic bounds of moments for long range operators in arbitrary dimension
• Localization and IDS Regularity in the Disordered Hubbard Model within Hartree-Fock Theory
• A Lieb-Robinson bound for quantum spin chains with strong on-site impurities
• On the Regime of Localized Excitations for Disordered Oscillator Systems
• Entanglement Entropy Bounds in the Higher Spin XXZ Chain
• Localization in the random XXZ quantum spin chain
• Sub-ballistic operator growth in spin chains with heavy-tailed random fields
• Dynamical Evolution of Entanglement in Disordered Oscillator Systems
• Vanishing of Drude weight in interacting fermions on Zd with quasi-periodic disorder