来自纠缠的聚变规则
Fusion rules from entanglement
摘要：
我们导出了任意子代数理论的一些公理[A. Kitaev，Ann. Phys.，321，2（2006）]从二维带隙系统的纠缠面积定律的简化形式。我们导出了拓扑荷的融合规则，并证明了融合规则的重数满足这些公理。此外，即使我们没有假设盘状区域纠缠熵的常数子前导项的确切值，该项也被证明等于$\ln \mathcal{D}$，其中$\mathcal{D}$是基础任意子理论的总量子维数。这些推导是严格的，并遵循纠缠区法律。更确切地说，我们的框架从两个局部熵约束，这是隐含的面积定律。从这些约束，我们证明了我们所说的“同构定理。“超选择扇区和聚变多重性的存在是从这个定理得出的，即使没有对父哈密顿量做任何假设。这些对象和公理的任意子理论的信息凸集的结构和内部的自洽关系。
英文摘要：
We derive some of the axioms of the algebraic theory of anyon [A. Kitaev, Ann. Phys., 321, 2 (2006)] from a conjectured form of entanglement area law for two-dimensional gapped systems. We derive the fusion rules of topological charges and show that the multiplicities of the fusion rules satisfy these axioms. Moreover, even though we make no assumption about the exact value of the constant sub-leading term of the entanglement entropy of a disk-like region, this term is shown to be equal to $\ln \mathcal{D}$, where $\mathcal{D}$ is the total quantum dimension of the underlying anyon theory. These derivations are rigorous and follow from the entanglement area law alone. More precisely, our framework starts from two local entropic constraints, which are implied by the area law. From these constraints, we prove what we refer to as the "isomorphism theorem." The existence of superselection sectors and fusion multiplicities follows from this theorem, even without assuming anything about the parent Hamiltonian. These objects and the axioms of the anyon theory are shown to emerge from the structure and the internal self-consistency relations of the information convex sets.
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