论文标题
开放xxz自旋的相关函数1/2量子链与非平行边界磁场
Correlation functions for open XXZ spin 1/2 quantum chains with unparallel boundary magnetic fields
论文作者
论文摘要
在本文中，我们继续推导开放量子自旋1/2链的相关函数，边缘在边缘上具有无与伦比的磁场。这次是XXZ旋转1/2链的更多情况。我们在变量（SOV）的量子分离框架中开发了研究，这为我们提供了完整的频谱表征和简单的标量产品公式，包括单独的状态，包括传递矩阵特征态。在这里，我们将边界磁场留在链的第一个站点中，完全任意任意，并将链条的最后一个站点$ n $固定为沿$ z $方向的特定值。这是无与伦比的边界磁场的自然首选。我们证明，在这些特殊的边界条件下，在一侧，我们在均匀的百特（例如$ tq $ equation）方面具有足够简单的完整频谱描述。另一方面，我们证明了本地运算符基础对传输矩阵本特征状态的基础的作用的简单描述，作为单独状态的线性组合。借助这些结果，我们实现了我们的主要目标，可以为有限和半限制链的一组本地运营商提供相关功能，并在最后一个情况下具有多个积分公式。
In this paper we continue our derivation of the correlation functions of open quantum spin 1/2 chains with unparallel magnetic fields on the edges; this time for the more involved case of the XXZ spin 1/2 chains. We develop our study in the framework of the quantum Separation of Variables (SoV), which gives us both the complete spectrum characterization and simple scalar product formulae for separate states, including transfer matrix eigenstates. Here, we leave the boundary magnetic field in the first site of the chain completely arbitrary, and we fix the boundary field in the last site $N$ of the chain to be a specific value along the $z$-direction. This is a natural first choice for the unparallel boundary magnetic fields. We prove that under these special boundary conditions, on the one side, we have a simple enough complete spectrum description in terms of homogeneous Baxter like $TQ$-equation. On the other side, we prove a simple enough description of the action of a basis of local operators on transfer matrix eigenstates as linear combinations of separate states. Thanks to these results, we achieve our main goal to derive correlation functions for a set of local operators both for the finite and half-infinite chains, with multiple integral formulae in this last case.
