基于超图分解的链接簇扩展
Linked Cluster Expansions via Hypergraph Decompositions
摘要：
我们提出了一个超图展开，这有利于直接处理量子自旋模型与多站点相互作用通过微扰连接集群的扩展。其主要思想是生成所有相关的子集群，并将它们分类到本质上由超图同构控制的等价类中。具体地说，一个简化的König表示的超图是用来使等价关系可图同构。在此过程中，我们确定每个等价类的嵌入因子，该因子用于最终的重新确定以获得最终结果。作为一个有指导意义的例子，我们计算了三维立方晶格上横场中的元胞伊辛模型的基态能量和特定的激发能隙。
英文摘要：
We propose a hypergraph expansion which facilitates the direct treatment of quantum spin models with many-site interactions via perturbative linked cluster expansions. The main idea is to generate all relevant subclusters and sort them into equivalence classes essentially governed by hypergraph isomorphism. Concretely, a reduced König representation of the hypergraphs is used to make the equivalence relation accessible by graph isomorphism. During this procedure we determine the embedding factor for each equivalence class, which is used in the final resummation in order to obtain the final result. As an instructive example we calculate the ground-state energy and a particular excitation gap of the plaquette Ising model in a transverse field on the three-dimensional cubic lattice.
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