论文标题
在标量产品和形态上通过变量分开：反碘XXZ模型
On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
论文作者
论文摘要
我们考虑具有反碘边界条件的XXZ Spin-1/2 Heisenberg链。该模型的不均匀版本可以通过变量的分离（SOV）来求解，并且可以根据Q-函数来构建本征态，即Baxter TQ-方程的解决方案，与周期案例相比具有双重周期性。我们在此框架中计算特定类别的单独状态的标量产品，这些状态特别包括传输矩阵的本征状态。我们还计算了局部自旋算子的形式，即它们的矩阵元素之间的矩阵元素之间的两个特征矩阵之间的元素。我们表明，这些数量以行和列标记为相应单独状态的Q-函数的根和列标记的列的行列表示形式，尽管在此期刊中，尽管确定性的形式在这里略有不同。我们还提出了直接根据转移矩阵特征值编写的替代类型的决定性表示形式。
We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by Separation of Variables (SoV), and the eigenstates can be constructed in terms of Q-functions, solution of a Baxter TQ-equation, which have double periodicity compared to the periodic case. We compute in this framework the scalar products of a particular class of separate states which notably includes the eigenstates of the transfer matrix. We also compute the form factors of local spin operators, i.e. their matrix elements between two eigenstates of the transfer matrix. We show that these quantities admit determinant representations with rows and columns labelled by the roots of the Q-functions of the corresponding separate states, as in the periodic case, although the form of the determinant are here slightly different. We also propose alternative types of determinant representations written directly in terms of the transfer matrix eigenvalues.
