Manifestations of dynamical localization in the disordered XXZ spin chain

TL;DR

This paper demonstrates how disordered XXZ spin chains exhibit dynamical localization phenomena within a specific energy range, including non-spreading of information and zero-velocity bounds, without requiring knowledge outside this range.

Contribution

It proves dynamical localization manifestations in the droplet spectrum of disordered XXZ spin chains, extending understanding of localization phenomena in these models.

Findings

Non-spreading of information in the droplet spectrum

Zero-velocity Lieb-Robinson bounds established

Localization restricted to the droplet spectrum

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.