Many-body localization in the droplet spectrum of the random XXZ quantum spin chain

TL;DR

This paper proves exponential clustering of eigenstates in the droplet spectrum of the disordered XXZ spin chain, demonstrating many-body localization properties in the Ising phase with strong disorder.

Contribution

It establishes a rigorous exponential clustering result for eigenstates in the droplet spectrum of the disordered XXZ chain, applicable in large disorder and strong Ising phase regimes.

Findings

Exponential decay of correlators in eigenstates over distance

Persistence of exponential clustering under time evolution

Results hold uniformly in disorder strength and observable support

Abstract

We study many-body localization properties of the disordered XXZ spin chain in the Ising phase. Disorder is introduced via a random magnetic field in the $z$-direction. We prove a strong form of dynamical exponential clustering for eigenstates in the droplet spectrum: For any pair of local observables separated by a distance $\ell$, the sum of the associated correlators over these states decays exponentially in $\ell$, in expectation. This exponential clustering persists under the time evolution in the droplet spectrum. Our result applies to the large disorder regime as well as to the strong Ising phase at fixed disorder, with bounds independent of the support of the observables.