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

Alexander Elgart, Abel Klein, Günter Stolz

Research output: Contribution to journalArticlepeer-review

20 Scopus citations


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 ℓ, the sum of the associated correlators over these states decays exponentially in ℓ, 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.

Original languageEnglish
Pages (from-to)211-258
Number of pages48
JournalJournal of Functional Analysis
Issue number1
StatePublished - 1 Jul 2018
Externally publishedYes


  • Droplet spectrum
  • Exponential clustering
  • Many-body localization
  • XXZ chain in a random field

ASJC Scopus subject areas

  • Analysis


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