Kitaev model in regular hyperbolic tilings
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909893100830720 |
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| author | Vidal, Julien Mosseri, Rémy |
| author_facet | Vidal, Julien Mosseri, Rémy |
| contents | We study the Kitaev model on regular hyperbolic trivalent tilings. Depending on the length $p$ of the elementary polygons, we examine two distinct tri-colorings of the tiling. Using a recent conjecture on the ground-state flux sector, we compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians in the isolated-dimer limit which are valid for all values of $p$. Our results interpolate between the Euclidean honeycomb lattice and the trivalent Bethe lattice ($p=\infty$) for which we derive the exact solution of the phase boundaries. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_17981 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Kitaev model in regular hyperbolic tilings Vidal, Julien Mosseri, Rémy Strongly Correlated Electrons Quantum Physics We study the Kitaev model on regular hyperbolic trivalent tilings. Depending on the length $p$ of the elementary polygons, we examine two distinct tri-colorings of the tiling. Using a recent conjecture on the ground-state flux sector, we compute the phase diagram via exact diagonalizations and derive analytical expressions for the effective Hamiltonians in the isolated-dimer limit which are valid for all values of $p$. Our results interpolate between the Euclidean honeycomb lattice and the trivalent Bethe lattice ($p=\infty$) for which we derive the exact solution of the phase boundaries. |
| title | Kitaev model in regular hyperbolic tilings |
| topic | Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2506.17981 |