Many-body Localization and Poisson statistics in the Quantum Sun model
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866913895951630336 |
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| author | De Roeck, Wojciech Hannani, Amirali |
| author_facet | De Roeck, Wojciech Hannani, Amirali |
| contents | The Quantum Sun model is a many-body Hamiltonian model of interacting spins arranged on the half-line. Spins at distance $n$ from the origin are coupled to the rest of the system via a term of strength $α^n$, with $α\in (0,1)$. From theoretical and numerical considerations, it is believed that this model undergoes a localization-delocalization transition at the critical value $α=\frac{1}{\sqrt{2}}$. We prove that, for $α\ll \frac{1}{\sqrt{2}}$, the model is localized and that its spectral statistics is Poissonian. The main interest of this result is that the model is a genuine many-body model. In particular, the number of independent disorder variables grows only logarithmically with the Hilbert space dimension. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_13511 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Many-body Localization and Poisson statistics in the Quantum Sun model De Roeck, Wojciech Hannani, Amirali Mathematical Physics The Quantum Sun model is a many-body Hamiltonian model of interacting spins arranged on the half-line. Spins at distance $n$ from the origin are coupled to the rest of the system via a term of strength $α^n$, with $α\in (0,1)$. From theoretical and numerical considerations, it is believed that this model undergoes a localization-delocalization transition at the critical value $α=\frac{1}{\sqrt{2}}$. We prove that, for $α\ll \frac{1}{\sqrt{2}}$, the model is localized and that its spectral statistics is Poissonian. The main interest of this result is that the model is a genuine many-body model. In particular, the number of independent disorder variables grows only logarithmically with the Hilbert space dimension. |
| title | Many-body Localization and Poisson statistics in the Quantum Sun model |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2506.13511 |