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

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.

The main result now proves {\it dynamical} exponential clustering. 34 pages, no figures

References in corpus (8)

• Localization of interacting fermions at high temperature
• Many-body localization edge in the random-field Heisenberg chain
• Many body localization in Heisenberg XXZ magnet in a random field
• Lieb-Robinson Bounds and the Exponential Clustering Theorem
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Cited by in corpus (2)

• Bounds on the entanglement entropy of droplet states in the XXZ spin chain
• Slow propagation in some disordered quantum spin chains