Integrable models on Rydberg atom chains
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866916711280672768 |
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| author | Corcoran, Luke de Leeuw, Marius Pozsgay, Balázs |
| author_facet | Corcoran, Luke de Leeuw, Marius Pozsgay, Balázs |
| contents | We initiate a systematic study of integrable models for spin chains with constrained Hilbert spaces; we focus on spin-1/2 chains with the Rydberg constraint. We extend earlier results for medium-range spin chains to the constrained Hilbert space, and formulate an integrability condition. This enables us to construct new integrable models with fixed interaction ranges. We classify all time- and space-reflection symmetric integrable Rydberg-constrained Hamiltonians of range 3 and 4. At range 3, we find a single family of integrable Hamiltonians: the so-called RSOS quantum chains, which are related to the well-known RSOS models of Andrews, Baxter, and Forrester. At range 4 we find two families of models, the first of which is the constrained XXZ model. We also find a new family of models depending on a single coupling $z$. We provide evidence of two critical points related to the golden ratio $ϕ$, at $z=ϕ^{-1/2}$ and $z=ϕ^{3/2}$. We also perform a partial classification of integrable Hamiltonians for range 5. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2405_15848 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Integrable models on Rydberg atom chains Corcoran, Luke de Leeuw, Marius Pozsgay, Balázs Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems We initiate a systematic study of integrable models for spin chains with constrained Hilbert spaces; we focus on spin-1/2 chains with the Rydberg constraint. We extend earlier results for medium-range spin chains to the constrained Hilbert space, and formulate an integrability condition. This enables us to construct new integrable models with fixed interaction ranges. We classify all time- and space-reflection symmetric integrable Rydberg-constrained Hamiltonians of range 3 and 4. At range 3, we find a single family of integrable Hamiltonians: the so-called RSOS quantum chains, which are related to the well-known RSOS models of Andrews, Baxter, and Forrester. At range 4 we find two families of models, the first of which is the constrained XXZ model. We also find a new family of models depending on a single coupling $z$. We provide evidence of two critical points related to the golden ratio $ϕ$, at $z=ϕ^{-1/2}$ and $z=ϕ^{3/2}$. We also perform a partial classification of integrable Hamiltonians for range 5. |
| title | Integrable models on Rydberg atom chains |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.15848 |