论文标题
$ [d+1] $ dimensions中的集成性：转移矩阵的局部方程式和通勤性
Integrability in $[d+1]$ dimensions: combined local equations and commutativity of the transfer matrices
论文作者
论文摘要
我们建议在代数贝尔斯ansatz（ABA）框架中的统计顶点模型（ABA）中的统计顶点模型。对于低维案例，显示了转移矩阵换向的逐步考虑的效率。我们使用某些20-Vertex结构的三态$ r $ $ - 构建一些简单的3D解决方案；讨论了与量子三分之三门的连接。还定义了具有四态$ r $ - matrices的3D局部集成性方程的新版本。然后，我们构建了二维星形三角方程的新3D类似物。
We propose new inhomogeneous local integrability equations - combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low dimensional cases the efficiency of the step by step consideration of the transfer matrices' commutation is demonstrated. We construct some simple 3D solutions with the three-state $R$-matrices of certain 20-vertex structure; the connection with the quantum three-qubit gates is discussed. New, restricted versions of 3D local integrability equations with four-state $R$-matrices are defined, too. Then we construct a new 3D analogue of the two-dimensional star-triangle equations.
