We derive some of the axioms of the algebraic theory of anyon (Kitaev, 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 D, where 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 multiplicites follow 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.

中文翻译：

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纠缠的融合规则

我们从二维有隙系统的纠缠面积定律的一种推测形式中推导出了任意子代数理论的一些公理（Kitaev，2006）。我们推导出拓扑荷的融合规则，并证明融合规则的多重性满足这些公理。此外，即使我们不假设盘状区域纠缠熵的常数次导项的确切值，该项也被证明等于 ln D，其中 D 是该区域的总量子维数。任何人理论的基础。这些推导是严格的，并且仅遵循纠缠区定律。更准确地说，我们的框架从面积定律隐含的两个局部熵约束开始。根据这些约束，我们证明了我们所说的“同构定理”。” 超选择扇区和融合乘数的存在来自这个定理，即使不假设任何关于父哈密顿量的东西。这些对象和任意子理论的公理被证明是从信息凸集的结构和内部自洽关系中出现的。