Droplet localization in the random XXZ model and its manifestations

TL;DR

This paper investigates many-body localization in the droplet sector of the random-field XXZ chain, demonstrating localization properties and dynamical consequences without relying on full spectral knowledge.

Contribution

It introduces a droplet sector localization framework for the XXZ model, deriving dynamical consequences based on a single cluster localization property.

Findings

Establishes dynamical exponential clustering.

Shows non-spreading of information under time evolution.

Derives a zero velocity Lieb-Robinson bound.

Abstract

We examine many-body localization properties for the eigenstates that lie in the droplet sector of the random-field spin-$\frac 1 2$ XXZ chain. These states satisfy a basic single cluster localization property (SCLP), derived in \cite{EKS}. This leads to many consequences, including dynamical exponential clustering, non-spreading of information under the time evolution, and a zero velocity Lieb Robinson bound. Since SCLP is only applicable to the droplet sector, our definitions and proofs do not rely on knowledge of the spectral and dynamical characteristics of the model outside this regime. Rather, to allow for a possible mobility transition, we adapt the notion of restricting the Hamiltonian to an energy window from the single particle setting to the many body context.