标题： 表征拓扑纠缠熵的模糊性 显示英文标题

标题： Characterizing the ambiguity in topological entanglement entropy

摘要： 拓扑纠缠熵（TEE），即拓扑序的纠缠熵中的次主导项，是长程纠缠的直接证据。 虽然在表征闭流形上的拓扑序方面有效，但当纠缠切分与物理能隙边界相交时，TEE是模型相关的。 在本文中，我们通过引入一种与模型无关的、用能隙边界划分拓扑序的图像，研究这种模型相关性的起源。 在我们的图像中，纠缠边界（EBs），即由纠缠切分引起的每个子系统的虚拟边界，被假定为具有边界缺陷的能隙边界。 在这个与模型无关的阶段，定义双分割时需要手动做出两个选择：EBs上的边界条件，以及某些边界态之间的相干性。 我们证明，TEE的出现是由于EBs上缺陷配置的约束，而在EBs接触能隙边界的情况下，这种约束是选择相关的。 这种选择相关性被称为纠缠熵中的歧义性。 不同的模型本质上采用不同的选择，使得TEE成为模型相关的。 对于Z2表面码，这种歧义性可以通过两个参数完全表征，分别量化EB条件和相干性。 特别是，与折叠技巧相容的计算自然选择尊重电-磁对偶性的EB条件，并设定特定的参数值。 显示英文摘要

摘要： Topological entanglement entropy (TEE), the sub-leading term in the entanglement entropy of topological order, is the direct evidence of the long-range entanglement. While effective in characterizing topological orders on closed manifolds, TEE is model-dependent when entanglement cuts intersect with physical gapped boundaries. In this paper, we study the origin of this model-dependence by introducing a model-independent picture of partitioning the topological orders with gapped boundaries. In our picture, the entanglement boundaries (EBs), i.e. the virtual boundaries of each subsystem induced by the entanglement cuts, are assumed to be gapped boundaries with boundary defects. At this model-independent stage, there are two choices one has to make manually in defining the bi-partition: the boundary condition on the EBs, and the coherence between certain boundary states. We show that TEE appears because of a constraint on the defect configurations on the EBs, which is choice-dependent in the cases where the EBs touch gapped boundaries. This choice-dependence is known as the ambiguity in entanglement entropy. Different models intrinsically employ different choices, rendering TEE model-dependent. For Z2 toric code, the ambiguity can be fully characterized by two parameters that respectively quantifies the EB condition and the coherence. In particular, calculations compatible with the folding trick naturally choose EB conditions that respect electric-magnetic duality and set specific parameter values.