标题： 开放的XYZ自旋1/2链：边界场满足约束条件时的分离变量和标量积 显示英文标题

标题： The open XYZ spin 1/2 chain: Separation of Variables and scalar products for boundary fields related by a constraint

摘要： 我们考虑具有边界场的开放XYZ自旋链。 我们通过在arXiv:1904.00852中引入的新变量分离方法解决了该模型。 在此框架中，转移矩阵本征态被作为所谓的分离态类的一个特定子类获得。 我们考虑计算此类分离态的标量积的问题。 通常，它们可以表示为行由模型的非均匀参数标记的行列式。 我们特别关注边界参数满足一个约束条件的特殊情况，这些边界参数参数化两个边界场，从而使得部分转移矩阵谱和本征态可以用某个通常TQ方程的椭圆多项式Q解来描述。 在这种情况下，我们展示了如何将上述标量积的行列式转换为更方便的形式，以便考虑齐次和热力学极限：如同开放XXX或XXZ情况一样，我们的结果可以表示为所谓的斯拉瓦诺夫行列式的某种推广。 显示英文摘要

摘要： We consider the open XYZ spin chain with boundary fields. We solve the model by the new Separation of Variables approach introduced in arXiv:1904.00852. In this framework, the transfer matrix eigenstates are obtained as a particular sub-class of the class of so-called separate states. We consider the problem of computing scalar products of such separate states. As usual, they can be represented as determinants with rows labelled by the inhomogeneity parameters of the model. We notably focus on the special case in which the boundary parameters parametrising the two boundary fields satisfy one constraint, hence enabling for the description of part of the transfer matrix spectrum and eigenstates in terms of some elliptic polynomial Q-solution of a usual TQ-equation. In this case, we show how to transform the aforementioned determinant for the scalar product into some more convenient form for the consideration of the homogeneous and thermodynamic limits: as in the open XXX or XXZ cases, our result can be expressed as some generalisation of the so-called Slavnov determinant.