标题： 二维系统中的纠缠角依赖性：张量网络视角 显示英文标题

标题： Entanglement corner dependence in two-dimensional systems: A tensor network perspective

摘要： 在连续量子场论中，具有尖角边界的部分子系统的纠缠熵表现出一个与角落相关的普遍贡献。 我们通过离散系统的视角来研究这一贡献，并证明这种角落依赖性自然地来源于离散格点上无限投影纠缠对态（iPEPS）的几何结构。 通过严格的计数论证，我们表明iPEPS表示的键维数表现出一个与角落相关的项，该项与间隙连续系统中的预测项相匹配。 关键的是，我们发现只有在对所有可能的格点方向进行平均时，这种对应关系才会出现，这揭示了正确离散化连续系统的基本要求。 我们的结果提供了对纠缠角落定律的几何理解，并建立了分析场论预测与张量网络表示结构之间的直接联系。 我们将分析扩展到规范不变系统，在这种系统中，被分割边界穿过的格点角落会贡献一个额外的与角落相关的项。 这些发现为连续和离散量子系统中的纠缠关系提供了新的见解。 显示英文摘要

摘要： In continuous quantum field theories, the entanglement entropy of a subsystem with sharp corners in its boundary exhibits a universal corner-dependent contribution. We study this contribution via the lens of discretized systems, and demonstrate that this corner dependence emerges naturally from the geometric structure of infinite projected entangled pair states (iPEPS) on discrete lattices. Using a rigorous counting argument, we show that the bond dimension of an iPEPS representation exhibits a corner-dependent term that matches the predicted term in gapped continuous systems. Crucially, we find that this correspondence only emerges when averaging over all possible lattice orientations, revealing a fundamental requirement for properly discretizing continuous systems. Our results provide a geometric understanding of entanglement corner laws and establish a direct connection between analytical field theory predictions and the structure of tensor network representations. We extend our analysis to gauge-invariant systems, where lattice corners crossed by the bipartition boundary contribute an additional corner-dependent term. These findings offer new insights into the relationship between entanglement in continuous and discrete quantum systems.