任意链中典型纠缠：Lie 群对称性之外的 Page 曲线

我们研究一维任意链中的二分纠缠统计，其 Hilbert 空间受 unitary pre-modular categories 融合规则约束。Our setup generalizes previous frameworks on symmetry-resolved entanglement entropy for non-abelian Lie group symmetries to the setting of quantum groups. We derive analytical expressions for the average anyonic entanglement entropy and its variance. Surprisingly, despite the constrained Hilbert space structure, the large $L$ expansion has no universal $O(\sqrt{L})$ or $O(1)$ symmetry-type corrections except for a subleading topological correction term that produces a Page curve asymmetry. We further show that the variance decays exponentially with system size, establishing the typicality. Numerical simulations of the integrable and quantum-chaotic golden chain Hamiltonian show that chaotic mid-spectrum eigenstates match the Haar-random predictions, supporting the use of eigenstate entanglement as a diagnostic of quantum chaos. Our results establish the anyonic Page curve as an appropriate chaotic benchmark in topological many-body systems and connect anyonic entanglement to Page-type universality in quantum many-body physics.