Localization phenomena in the random XXZ spin chain
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arXiv
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| Auteurs principaux: | , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866912735818678272 |
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| author | Elgart, Alexander Klein, Abel |
| author_facet | Elgart, Alexander Klein, Abel |
| contents | It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of the parameter space. This region depends only on the energy interval and includes weak interaction and strong disorder regimes. The crucial step in the argument is a proof that if the Green functions for the associated finite systems Hamiltonians exhibit certain (volume-dependent) decay properties in a fixed energy interval, then the infinite volume Green function decays in the same interval as well. The pertinent finite systems decay properties for the random XXZ spin chain had been previously verified by the authors. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2502_01831 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Localization phenomena in the random XXZ spin chain Elgart, Alexander Klein, Abel Mathematical Physics 82B44, 82C44, 81Q10, 47B80, 60H25 It is shown that the infinite random Heisenberg XXZ spin-$\frac12$ chain exhibits localization phenomena, such as spectral, eigenstate, and weak dynamical localization, in an arbitrary (but fixed) energy interval in a non-trivial region of the parameter space. This region depends only on the energy interval and includes weak interaction and strong disorder regimes. The crucial step in the argument is a proof that if the Green functions for the associated finite systems Hamiltonians exhibit certain (volume-dependent) decay properties in a fixed energy interval, then the infinite volume Green function decays in the same interval as well. The pertinent finite systems decay properties for the random XXZ spin chain had been previously verified by the authors. |
| title | Localization phenomena in the random XXZ spin chain |
| topic | Mathematical Physics 82B44, 82C44, 81Q10, 47B80, 60H25 |
| url | https://arxiv.org/abs/2502.01831 |