论文标题
2D对称性受保护拓扑状态的对称分辨纠缠
Symmetry-resolved entanglement of 2D symmetry-protected topological states
论文作者
论文摘要
对称分辨的纠缠是表征对称对称性拓扑状态的有用工具。在两个维度中，它们的纠缠光谱是通过共形场理论描述的，但对称分辨率在很大程度上没有探索。但是，在数值上解决此问题需要超出精确对角线化的系统大小。在这里，我们开发了张量的网络方法，这些方法可以访问更大的系统并确定其纠缠中的通用和非宇宙特征。具体而言，我们构建了一维矩阵产品运算符，以封装二维对称性保护拓扑状态的所有纠缠数据。我们首先演示了Levin-GU模型的方法。接下来，我们使用共同的形式主义将阶段从微调点变形，并跟踪其纠缠特征和对称性分辨率的演变。纠缠光谱始终由相同的保形场理论描述。然而，根据插入多体aharonov-bohm通量的水平流量。
Symmetry-resolved entanglement is a useful tool for characterizing symmetry-protected topological states. In two dimensions, their entanglement spectra are described by conformal field theories but the symmetry resolution is largely unexplored. However, addressing this problem numerically requires system sizes beyond the reach of exact diagonalization. Here, we develop tensor network methods that can access much larger systems and determine universal and nonuniversal features in their entanglement. Specifically, we construct one-dimensional matrix product operators that encapsulate all the entanglement data of two-dimensional symmetry-protected topological states. We first demonstrate our approach for the Levin-Gu model. Next, we use the cohomology formalism to deform the phase away from the fine-tuned point and track the evolution of its entanglement features and their symmetry resolution. The entanglement spectra are always described by the same conformal field theory. However, the levels undergo a spectral flow in accordance with an insertion of a many-body Aharonov-Bohm flux.
