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<p>We show that every fusion category containing a non-invertible, self-dual object <i>a</i> 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 <i>a</i> ⨂ <i>a</i>. 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 <i>a</i> is greater than 2. We show that for fusion categories where the dimension is close to 2, such as the Fib×Fib and Haagerup fusion categories, the finite size effects are large and they can obscure the numerical analysis of the gap.</p>

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Temperley-Lieb integrable models and fusion categories

  • 期刊论文

  • 出版模式：

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  • 发表日期：

    2026年4月20日

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  • Matthew Blakeney,
  • Luke Corcoran,
  • Marius de Leeuw,
  • Balázs Pozsgay,
  • Eric Vernier

摘要

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 ⨂ 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×Fib and Haagerup fusion categories, the finite size effects are large and they can obscure the numerical analysis of the gap.