Geodesic
Localization in the random XXZ quantum spin chain
Forum of Mathematics, Sigma, Tome 12 (2024)

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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. 
@article{10_1017_fms_2024_119,
     author = {Alexander Elgart and Abel Klein},
     title = {Localization in the random {XXZ} quantum spin chain},
     journal = {Forum of Mathematics, Sigma},
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     doi = {10.1017/fms.2024.119},
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Alexander Elgart; Abel Klein. Localization in the random XXZ quantum spin chain. Forum of Mathematics, Sigma, Tome 12 (2024). doi: 10.1017/fms.2024.119

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