双曲张量网络的顶点表示
Vertex Representation of Hyperbolic Tensor Networks
AI总结：
本文提出双曲晶格经典自旋系统的顶点型张量网络表示，证明纠缠熵可区分双曲几何，并验证其在各级相变中的数值精度与量子基态应用潜力。
摘要：
我们提出了一种张量网络（TN）的顶点表示，用于双曲晶格上的经典自旋系统。这些张量构成一个由正p边形（p>4）组成、配位数为4的网络。我们在整个参数空间内分析了双曲TN对多态自旋系统的响应。结果表明，纠缠熵能够灵敏地区分各种双曲几何，而其他热力学量则不能。我们在最大纠缠熵点处，测试了顶点TN在一级、二级和无穷级相变中的数值精度。TN的双曲结构在体相中诱导出非临界性质，尽管在热力学极限下边界条件会显著影响总自由能。因此，所发展的顶点型TN可用于研究双曲晶格上的最低能量子态。
英文摘要：
We propose a vertex representation of the tensor network (TN) for classical spin systems on hyperbolic lattices. The tensors form a network of regular $p$-sided polygons ($p>4$) with the coordination number four. The response to multi-state spin systems on the hyperbolic TN is analyzed for their entire parameter space. We show that entanglement entropy is sensitive to distinguish various hyperbolic geometries whereas other thermodynamic quantities are not. We test the numerical accuracy of vertex TNs in the phase transitions of the first, second, and infinite order at the point of maximal entanglement entropy. The hyperbolic structure of TNs induces non-critical properties in the bulk although boundary conditions significantly affect the total free energy in the thermodynamic limit. Thus developed vertex-type TN can be used for the lowest-energy quantum states on the hyperbolic lattices.
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