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arXiv · 2510.19902

Temperley-Lieb integrable models and fusion categories

Matthew Blakeney·Luke Corcoran·Marius de Leeuw·Balazs Pozsgay·Eric Vernier
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Abstract

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.

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Matthew Blakeney, Luke Corcoran, Marius de Leeuw, Balazs Pozsgay, Eric Vernier. 2025-10-22. Temperley-Lieb integrable models and fusion categories. https://arxiv.org/abs/2510.19902

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