Temperley-Lieb integrable models and fusion categories
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866908779896897536 |
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| author | Blakeney, Matthew Corcoran, Luke de Leeuw, Marius Pozsgay, Balazs Vernier, Eric |
| author_facet | Blakeney, Matthew Corcoran, Luke de Leeuw, Marius Pozsgay, Balazs Vernier, Eric |
| contents | We show that every fusion category containing a non-invertible, self-dual object $a$ gives rise to an integrable anyonic chain whose Hamiltonian density satisfies the Temperley-Lieb algebra. This spin chain arises by considering the projection onto the identity channel in the fusion process $a\otimes a$. We relate these models to Pasquier's construction of ADE lattice models. We then exploit the underlying Temperley-Lieb structure to discuss the spectrum of these models and argue that these models are gapped when the quantum dimension of $a$ is greater than 2. We show that for fusion categories where the dimension is close to 2, such as the Fib$\times$Fib and Haagerup fusion categories, the finite size effects are large and they can obscure the numerical analysis of the gap. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_19902 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Temperley-Lieb integrable models and fusion categories Blakeney, Matthew Corcoran, Luke de Leeuw, Marius Pozsgay, Balazs Vernier, Eric Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems We show that every fusion category containing a non-invertible, self-dual object $a$ gives rise to an integrable anyonic chain whose Hamiltonian density satisfies the Temperley-Lieb algebra. This spin chain arises by considering the projection onto the identity channel in the fusion process $a\otimes a$. We relate these models to Pasquier's construction of ADE lattice models. We then exploit the underlying Temperley-Lieb structure to discuss the spectrum of these models and argue that these models are gapped when the quantum dimension of $a$ is greater than 2. We show that for fusion categories where the dimension is close to 2, such as the Fib$\times$Fib and Haagerup fusion categories, the finite size effects are large and they can obscure the numerical analysis of the gap. |
| title | Temperley-Lieb integrable models and fusion categories |
| topic | Strongly Correlated Electrons Statistical Mechanics High Energy Physics - Theory Mathematical Physics Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2510.19902 |