标题： 来自高阶形式对称性的纠缠求和规则 显示英文标题

标题： Entanglement Sum Rule from Higher-Form Symmetries

摘要： 我们证明了一个关于具有有限阿贝尔高形式对称性的$(d{-}1)$维量子格点模型的纠缠求和规则，该规则通过将携带$p$形式$G$对称性的$p$单纯形上的一个扇区与携带对偶$(d{-}p{-}2)$形式$\widehat G$对称性的$(p{+}1)$单纯形上的一个扇区进行最小耦合得到（其中$\widehat G$是$G$的庞特里亚金对偶）。 通过与保持对称性的算符$\mathcal{U}$进行共轭引入耦合，该算符将保持对称性的算符与适当的威尔逊算符结合。在保持对称性的子空间上，$\mathcal{U}$是良好定义的且是么正的，耦合哈密顿量通过与$\mathcal{U}$进行共轭从解耦的哈密顿量得到。我们的主要结果涉及通过作用于解耦模型的直积对称本征态上的$\mathcal{U}$而产生的耦合模型的对称本征态：如果所选二分法满足通过Mayer--Vietoris序列表述的拓扑条件，则当作用于对称态时，$\mathcal{U}$在切割处可分解，并且双部分纠缠熵等于两个部分熵的和。该框架解释并推广了费米子-$\mathbb{Z}_2$规范理论中的已知例子，确定了拓扑阻碍分解的情况，并提供了一种通过规范高阶对称性来构造新例子的方法。 显示英文摘要

摘要： We prove an entanglement sum rule for $(d{-}1)$-dimensional quantum lattice models with finite abelian higher-form symmetries, obtained by minimally coupling a sector on $p$-simplices carrying a $p$-form $G$ symmetry to a sector on $(p{+}1)$-simplices carrying the dual $(d{-}p{-}2)$-form $\widehat G$ symmetry (with $\widehat G$ the Pontryagin dual of $G$). The coupling is introduced by conjugation with a symmetry-preserving operator $\mathcal{U}$ that dresses symmetry-invariant operators with appropriate Wilson operators. On the symmetry-invariant subspace, $\mathcal{U}$ is well-defined and unitary, and the coupled Hamiltonian is obtained from the decoupled one by conjugation with $\mathcal{U}$. Our main result concerns symmetric eigenstates of the coupled model that arise by acting with $\mathcal{U}$ on direct-product, symmetric eigenstates of the decoupled model: provided a topological criterion formulated via the Mayer--Vietoris sequence holds for the chosen bipartition, $\mathcal{U}$ factorizes across the cut when acting on the symmetric state, and the bipartite entanglement entropy equals the sum of the entropies of the two sectors. The framework explains and generalizes known examples in fermion-$\mathbb{Z}_2$ gauge theory, identifies when topology obstructs the factorization, and provides a procedure to construct new examples by gauging higher-form symmetries.