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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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Slow Propagation of Information on the Random XXZ Quantum Spin Chain
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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- Award ID(s):
- 2307093
- PAR ID:
- 10620649
- Publisher / Repository:
- Springer Nature
- Date Published:
- Journal Name:
- Communications in Mathematical Physics
- Volume:
- 405
- Issue:
- 10
- ISSN:
- 0010-3616
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s00220-024-05127-y
