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  • Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
Title: Low-frequency behavior of off-diagonal matrix elements in the integrable XXZ chain and in a locally perturbed quantum-chaotic XXZ chain
Award ID(s):
1707482
PAR ID:
10288203
Author(s) / Creator(s):
; ;
Date Published:
Journal Name:
Physical Review B
Volume:
102
Issue:
7
ISSN:
2469-9950
Format(s):
Medium: X
Sponsoring Org:
National Science Foundation
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  1. ; (, Forum of Mathematics, Sigma)
    Abstract We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$$\frac 12$$chain in a random magnetic field. We prove that the system exhibits localization in any given energy interval at the bottom of the spectrum in a nontrivial region of the parameter space. This region, which includes weak interaction and strong disorder regimes, is independent of the size of the system and depends only on the energy interval. Our approach is based on the reformulation of the localization problem as an expression of quasi-locality for functions of the random many-body XXZ Hamiltonian. This allows us to extend the fractional moment method for proving localization, previously derived in a single-particle localization context, to the many-body setting. 
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  2. ; (, Communications in Mathematical Physics)
    The random XXZ quantum spin chain manifests localization (in the form of quasi-locality) in any fixed energy interval, as previously proved by the authors. In this article it is shown that this property implies slow propagation of information, one of the putative signatures of many-body localization (MBL), in the same energy interval. 
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    null (Ed.)
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