Tensor network states provide successful descriptions of strongly correlated quantum systems with applications ranging from condensed matter physics to cosmology. Any family of tensor network states possesses an underlying entanglement structure given by a graph of maximally entangled states along the edges that identify the indices of the tensors to be contracted. Recently, more general tensor networks have been considered, where the maximally entangled states on edges are replaced by multipartite entangled states on plaquettes. Both the structure of the underlying graph and the dimensionality of the entangled states influence the computational cost of contracting these networks. Using the geometrical properties of entangled states, we provide a method to construct tensor network representations with smaller effective bond dimension. We illustrate our method with the resonating valence bond state on the kagome lattice.

中文翻译：

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纠缠态的张量网络表示

张量网络状态提供了强相关量子系统的成功描述，其应用范围从凝聚态物理到宇宙学。张量网络状态的任何族都有一个基本的纠缠结构，该纠缠结构由沿着边缘的最大纠缠状态的图给出，该图标识了要收缩的张量的索引。近来，已经考虑了更通用的张量网络，其中边缘上的最大缠结状态被球拍上的多部分缠结状态代替。基础图的结构和纠缠态的维数都会影响收缩这些网络的计算成本。利用纠缠态的几何性质，我们提供了一种构造具有较小有效键维的张量网络表示的方法。