2025/10/22 by Blakeney, Matthew, Corcoran, Luke, de Leeuw, Marius +2
#Exactly Solvable and Integrable Systems (nlin.SI) #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Statistical Mechanics (cond-mat.stat-mech) #Strongly Correlated Electrons (cond-mat.str-el)
paper · doi:10.48550/arxiv.2510.19902
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.