具有 Ising 融合范式对称性的量子簇态自旋链：来自弱 Hopf 对称拓扑场论的视角

本文提出了一种展示 Ising 融合代数对称性的簇态晶格哈密顿量的构造。该构造在弱 Hopf 对称拓扑场论 (SymTFT) 框架内进行，其中我们为弱 Hopf 量子双模型分配平滑和粗糙边界，从而扩展了传统的簇态模型。我们构造的核心是弱 Hopf Ising 边界管道代数 $\mathcal{T}_{\mathsf{Ising}}$，其表示范畴等价于 Ising 融合范畴 $\mathsf{Ising}$。我们以该代数作为弱 Hopf 量子双模型的输入数据。 resulting model exhibits Ising fusion symmetry on both open and closed $1\text{d}$ manifolds. On open manifolds, the symmetry is governed by $\mathcal{T}_{\mathsf{Ising}} \otimes \mathcal{T}_{\mathsf{Ising}}^{\vee}$; on closed manifolds, it reduces to $\operatorname{Cocom}(\mathcal{T}_{\mathsf{Ising}}) \otimes \operatorname{Cocom}(\mathcal{T}_{\mathsf{Ising}}^{\vee})$. Since the Ising fusion algebra embeds into $\operatorname{Cocom}(\mathcal{T}_{\mathsf{Ising}}^{\vee})$, the model faithfully realizes the symmetry of the Ising fusion category.