This paper considers aspects of a Kagome lattice system with states classified by plane partitions. Using two sets of free fermions, we rewrite the lattice in terms of two families of spin chains. In this formalism, the quantum crystals Hamiltonian becomes more transparent, and we determine expressions for the first 3 levels of plane partition states. A classical statistical model associated to local configurations in the Kagome lattice is also defined, and we show that a reduction of this classical system gives two Yang-Baxter integrable subsystems analogous to a descendant of the 6-vertex model.

中文翻译：

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面向量子晶体熔化的Yang-Baxter可积性：从Kagome晶格到顶点模型

本文考虑状态按平面分区分类的Kagome晶格系统的各个方面。使用两组自由费米子，我们用两个自旋链族重写了晶格。在这种形式主义中，量子晶体哈密顿量变得更加透明，我们确定了平面划分态的前三个水平的表达式。还定义了与Kagome格中的局部配置相关的经典统计模型，并且我们证明了该经典系统的简化给出了两个Yang-Baxter可积子系统，类似于6顶点模型的后代。