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

Alexander Elgart, Abel Klein, Günter Stolz

Published 2017-03-22Version 1

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 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. 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.