Localization in the random XXZ quantum spin chain
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, wh...
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Cambridge University Press
2024-01-01
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| Series: | Forum of Mathematics, Sigma |
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| Online Access: | https://www.cambridge.org/core/product/identifier/S2050509424001191/type/journal_article |
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| author | Alexander Elgart Abel Klein |
| author_facet | Alexander Elgart Abel Klein |
| author_sort | Alexander Elgart |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-873f0bcbeefe4674a694c86c6f8cd6d0 |
| institution | Kabale University |
| issn | 2050-5094 |
| language | English |
| publishDate | 2024-01-01 |
| publisher | Cambridge University Press |
| record_format | Article |
| series | Forum of Mathematics, Sigma |
| spelling | doaj-art-873f0bcbeefe4674a694c86c6f8cd6d02025-01-16T21:47:58ZengCambridge University PressForum of Mathematics, Sigma2050-50942024-01-011210.1017/fms.2024.119Localization in the random XXZ quantum spin chainAlexander Elgart0https://orcid.org/0000-0002-8310-5654Abel Klein1https://orcid.org/0000-0002-4017-3286Department of Mathematics, Virginia Tech, Blacksburg, VA 24061-1026, USADepartment of Mathematics, University of California, Irvine, Irvine, CA 92697-3875, USA; E-mail: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.https://www.cambridge.org/core/product/identifier/S2050509424001191/type/journal_article82B4482C4481Q1047B8060H25 |
| spellingShingle | Alexander Elgart Abel Klein Localization in the random XXZ quantum spin chain Forum of Mathematics, Sigma 82B44 82C44 81Q10 47B80 60H25 |
| title | Localization in the random XXZ quantum spin chain |
| title_full | Localization in the random XXZ quantum spin chain |
| title_fullStr | Localization in the random XXZ quantum spin chain |
| title_full_unstemmed | Localization in the random XXZ quantum spin chain |
| title_short | Localization in the random XXZ quantum spin chain |
| title_sort | localization in the random xxz quantum spin chain |
| topic | 82B44 82C44 81Q10 47B80 60H25 |
| url | https://www.cambridge.org/core/product/identifier/S2050509424001191/type/journal_article |
| work_keys_str_mv | AT alexanderelgart localizationintherandomxxzquantumspinchain AT abelklein localizationintherandomxxzquantumspinchain |