Frustration-Free Models for Topological Holography: Fusion Spin Chains as Boundary Algebras

Abstract:We introduce a class of $2d$ quantum spin systems based on a unitary spherical fusion category with a chosen object. These models have frustration-free, reflection positive, but generally non-commuting local interactions, generalizing the Levin-Wen string-net models. Based on the theory developed in arXiv:2510.20662, we explicitly realize the Temperley-Lieb-Jones algebra, and more generally fusion spin chains as their boundary algebras.

32 pages, 5 figures. Comments welcome!

Mathematical Physics (math-ph); Strongly Correlated Electrons (cond-mat.str-el); Operator Algebras (math.OA); Quantum Physics (quant-ph)

arXiv:2609.28120 [math-ph]

(or arXiv:2609.28120v1 [math-ph] for this version)

https://doi.org/10.48550/arXiv.2609.28120 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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