We derive a refined version of the Affleck-Ludwig-Cardy formula for a 1+1D conformal field theory, which controls the asymptotic density of high energy states on an interval transforming under a given representation of a noninvertible global symmetry. We use this to determine the universal leading and subleading contributions to the noninvertible symmetry-resolved entanglement entropy of a single interval. As a concrete example, we show that the ground state entanglement Hamiltonian for a single interval in the critical double Ising model enjoys a Kac-Paljutkin H8 Hopf algebra symmetry when the boundary conditions at the entangling points are chosen to preserve the product of two Kramers-Wannier symmetries, and we present the corresponding symmetry-resolved entanglement entropies. Our analysis utilizes recent developments in symmetry topological field theories. Published by the American Physical Society 2024

中文翻译：

---

来自边界管代数的不可逆对称解析的 Affleck-Ludwig-Cardy 公式和纠缠熵


我们推导出了 1+1D 共形场论的 Affleck-Ludwig-Cardy 公式的改进版本，该公式控制在给定的不可逆全局对称性表示下变换的区间上高能态的渐近密度。我们用它来确定对单个区间的不可逆对称解析纠缠熵的普遍前导和次导贡献。作为一个具体的例子，我们表明，当选择纠缠点的边界条件以保持两个 Kramers-Wannier 对称性的乘积时，临界双 Ising 模型中单个区间的基态纠缠哈密顿量享有 Kac-Paljutkin H8 Hopf 代数对称性，并且我们提出了相应的对称解析纠缠熵。我们的分析利用了对称拓扑场论的最新发展。 美国物理学会 2024 年出版