Localization properties of the disordered XY spin chain

A review of mathematical results with an eye toward many-body localization

Houssam Abdul-Rahman, Bruno Nachtergaele, Robert J Sims, Günter Stolz

Research output: Contribution to journalReview article

15 Citations (Scopus)

Abstract

We review several aspects of Many-Body Localization-like properties exhibited by the disordered XY chains: localization properties of the energy eigenstates and thermal states, propagation bounds of Lieb-Robinson type, decay of correlation functions, absence of particle transport, bounds on the bipartite entanglement, and bounded entanglement growth under the dynamics. We also prove new results on the absence of energy transport and Fock space localization. All these properties are made accessible to mathematical analysis due to the exact mapping of the XY chain to a system of quasi-free fermions given by the Jordan-Wigner transformation. Motivated by these results we discuss conjectured properties of more general disordered quantum spin and other systems as possible directions for future mathematical research.

Original languageEnglish (US)
Article number1600280
JournalAnnalen der Physik
Volume529
Issue number7
DOIs
StatePublished - Jul 1 2017

Fingerprint

Jordan
applications of mathematics
eigenvectors
fermions
propagation
energy
decay

Keywords

  • Anderson Model
  • Area Law
  • Dynamical Localization
  • Entanglement Entropy
  • Fock Space Localization
  • Many-Body Localization
  • XY chain
  • Zero-Velocity Lieb-Robinson Bounds

ASJC Scopus subject areas

  • Physics and Astronomy(all)

Cite this

Localization properties of the disordered XY spin chain : A review of mathematical results with an eye toward many-body localization. / Abdul-Rahman, Houssam; Nachtergaele, Bruno; Sims, Robert J; Stolz, Günter.

In: Annalen der Physik, Vol. 529, No. 7, 1600280, 01.07.2017.

Research output: Contribution to journalReview article

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