标题： 量子化的环面六顶点模型 显示英文标题

标题： Quantized six-vertex model on a torus

摘要： 我们研究了在环面上具有四个参数的量子六顶点模型的可积性。 这是一个三维可积晶格模型，在该模型中，可以定义一个层转移矩阵，它依赖于与环面同调圈相关的两个光谱参数，不仅可以在正方形晶格上定义，也可以在更一般的图上定义。 对于一类我们称之为可容许的图，通过引入四种类型的四面体方程和两种类型的反演关系，我们建立了层转移矩阵的交换性。 在光谱参数上展开可以得到一族相互交换的量子哈密顿量。 量子六顶点模型还可以重新表述为（量子化的）二聚模型，并且作为特殊情况涵盖了已知的可积系统，包括自由参费米子模型和相对论性 Toda链。 显示英文摘要

摘要： We study the integrability of the quantized six-vertex model with four parameters on a torus. It is a three-dimensional integrable lattice model in which a layer transfer matrix, depending on two spectral parameters associated with the homology cycles of the torus, can be defined not only on the square lattice but also on more general graphs. For a class of graphs that we call admissible, we establish the commutativity of the layer transfer matrices by introducing four types of tetrahedron equations and two types of inversion relations. Expanding in the spectral parameters yields a family of commuting quantum Hamiltonians. The quantized six-vertex model can also be reformulated in terms of (quantized) dimer models, and encompasses known integrable systems as special cases, including the free parafermion model and the relativistic Toda chain.