论文标题
交错顶点模型的可整合边界条件
Integrable boundary conditions for staggered vertex models
论文作者
论文摘要
具有通用$ \ mathbb {z} _2 $ - 施加的Yang-baxter Antegrable Vertex模型可以用复合$ \ Mathbb {r} $ - 根据基本$ r $ -Matrices表示。类似地，可以基于这些对象及其表示形式来构建可集成的开放边界条件，以复合边界矩阵$ \ mathbb {k}^\ pm $来构建。我们表明，在这种方法中，只有两种类型的惊人产生了具有可整合的开放边界条件的当地哈密顿量。基础模型中的惊人允许第二个层次结构通勤积分（除了从通常的传输矩阵中获得的汉密尔顿人（包括从通常的转移矩阵获得的），从所谓的准势量运算符开始。在本文中，我们表明，可以从Yang-Baxter的放大或反射代数中以统一的方式与Hamiltonian一起获得该准动量运算符。对于交错的六个vertex模型的特殊情况，这允许在两个局部情况之间构建可集成的光谱流。
Yang-Baxter integrable vertex models with a generic $\mathbb{Z}_2$-staggering can be expressed in terms of composite $\mathbb{R}$-matrices given in terms of the elementary $R$-matrices. Similarly, integrable open boundary conditions can be constructed through generalized reflection algebras based on these objects and their representations in terms of composite boundary matrices $\mathbb{K}^\pm$. We show that only two types of staggering yield a local Hamiltonian with integrable open boundary conditions in this approach. The staggering in the underlying model allows for a second hierarchy of commuting integrals of motion (in addition to the one including the Hamiltonian obtained from the usual transfer matrix), starting with the so-called quasi momentum operator. In this paper, we show that this quasi momentum operator can be obtained together with the Hamiltonian for both periodic and open models in a unified way from enlarged Yang-Baxter or reflection algebras in the composite picture. For the special case of the staggered six-vertex model, this allows constructing an integrable spectral flow between the two local cases.
