Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
Baxter Q-operator and Separation of Variables for the open SL(2,R) spin chain
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开放 SL(2,R) 自旋链的 Baxter Q 算子和变量分离
DOI：
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发表时间：
2003
期刊：
影响因子：
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通讯作者：
A. Manashov
中科院分区：
文献类型：
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作者：
S. Derkachov;G. Korchemsky;A. Manashov
我们构造了齐次开SL(2，R)自旋链的Baxter Q−算符和分离变量(SOV)的表示。应用图解的方法，我们计算了分离变量中的Sklyanin积分测度，并根据Q−算子的本征值得到了该模型的谱问题的解。我们证明了到SOV表示的转换核被分解成某些运算符的乘积，每个运算符依赖于单个分离变量。因此，它具有一种普适的金字塔形状，这种形式已经在各种量子可积模型中观察到，如周期Toda链、闭合SL(2，R)和SL(2，C)自旋链。
: We construct the Baxter Q − operator and the representation of the Separated Variables (SoV) for the homogeneous open SL (2 , R ) spin chain. Applying the diagrammatical approach, we calculate Sklyanin’s integration measure in the separated variables and obtain the solution to the spectral problem for the model in terms of the eigenvalues of the Q − operator. We show that the transition kernel to the SoV representation is factorized into the product of certain operators each depending on a single separated variable. As a consequence, it has a universal pyramid-like form that has been already observed for various quantum integrable models such as periodic Toda chain, closed SL (2 , R ) and SL (2 , C ) spin chains.