Localization in the random XXZ quantum spin chain
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2022
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| _version_ | 1866909450044964864 |
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| author | Elgart, Alexander Klein, Abel |
| author_facet | Elgart, Alexander Klein, Abel |
| contents | We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$\frac12$ 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_14873 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Localization in the random XXZ quantum spin chain Elgart, Alexander Klein, Abel Mathematical Physics Spectral Theory Quantum Physics 82B44, 82C44, 81Q10, 47B80, 60H25 We study the many-body localization (MBL) properties of the Heisenberg XXZ spin-$\frac12$ 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. |
| title | Localization in the random XXZ quantum spin chain |
| topic | Mathematical Physics Spectral Theory Quantum Physics 82B44, 82C44, 81Q10, 47B80, 60H25 |
| url | https://arxiv.org/abs/2210.14873 |