开放XXZ链中的规范不变边界条件：SoV基、基本块与重叠
On the gauge invariant boundary condition in open XXZ chains: SoV bases, elementary blocks and overlaps
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中文总结 AI 辅助
该研究针对带非平行边界场的开放XXZ自旋链，在特定规范不变边界条件下，借助广义SoV方法对角化转移矩阵，推导SoV基的依赖关系，计算关联函数基本块及特定本征态重叠，丰富了XXZ自旋链的可解性研究。
中文摘要 AI 辅助
我们研究带有非平行边界场的开放XXZ自旋链，其特殊情形为：标记1位点边界场的K矩阵的Vertex-IRF变换是对角的，且在规范参数取值下不变，而另一个K矩阵是任意的。我们在此讨论与该特殊规范不变边界条件相关的若干性质。该模型可在带有任意规范参数的Vertex-IRF框架下求解：我们可通过广义Sklyanin变量分离（SoV）方法，在依赖两个任意规范参数α和β的SoV基族中对角化转移矩阵，其中β为所谓的动力学参数，α为谱参数的任意平移。我们在此表明，此类SoV基实际上仅通过差α-β依赖于α和β。考虑α-β趋于无穷的无规范极限，我们展示如何计算该模型关联函数的所有基本构建块。我们最后展示如何计算该模型本征态与某自旋链本征态之间的重叠，该自旋链在N位点处具有相同边界条件，且1位点处的规范不变边界条件已变更为更一般的形式。
英文摘要
We consider the open XXZ spin chain with unparallel boundary fields, in the special case in which the Vertex-IRF transform of the K-matrix labelling the boundary field at site 1 is diagonal and invariant under the value of the gauge parameters, the other K-matrix being arbitrary. We discuss here several properties related to this special gauge invariant boundary condition. Such a model can be solved in the Vertex-IRF framework with arbitrary gauge parameters: we can diagonalise the transfer matrix by means of generalised Sklyanin's Separation of Variable (SoV) approach in a family of SoV bases that depend on two arbitrary gauge parameters $α$ and $β$, $β$ being the so-called dynamical parameter and $α$ an arbitrary shift of the spectral parameter. We show here that such SoV bases depend actually on $α$ and $β$ through the difference $α-β$ only. Considering the ungauged limit in which $α-β$ tends to infinity, we show how to compute all elementary building blocks for the correlation functions of this model. We finally show how to compute overlaps between eigenstates of this model and eigenstates of a spin chain sharing the same boundary condition at site $N$ and in which the gauge invariant boundary condition at site 1 has been changed to a more general one.
