A Q -operator for the quantum transfer matrix
A Q -operator for the quantum transfer matrix
复制标题
量子转移矩阵的 Q 算子
DOI：
10.1088/1751-8113/40/14/002
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发表时间：
2007
期刊：
影响因子：
--
通讯作者：
Korff C
中科院分区：
文献类型：
--
作者：
Korff C
利用量子群的表示理论，将巴克斯特的Q算符概念推广到XXZ自旋链的量子转移矩阵.讨论了该Q算子的谱，并导出了描述XXZ自旋链有限温度区的新的函数关系。对于非零磁场，以前已知的Bethe anomaly方程可以用二次方程组代替，这对于数值研究是一个重要的优点。对于零磁场和有理耦合值，我们认为量子转移矩阵在单位根处表现出与经典六顶点转移矩阵密切相关的圈代数对称性。对于一些特殊的例子，还根据Q-算子的本征值讨论了量子-经典交叉。
Baxter's concept of a Q-operator is generalized to the quantum transfer matrix of the XXZ spin-chain by employing the representation theory of quantum groups. The spectrum of this Q-operator is discussed and novel functional relations which describe the finite temperature regime of the XXZ spin-chain are derived. For a non-vanishing magnetic field the previously known Bethe ansatz equations can be replaced by a system of quadratic equations which is an important advantage for numerical studies. For vanishing magnetic field and rational coupling values it is argued that the quantum transfer matrix exhibits a loop algebra symmetry closely related to the one of the classical six-vertex transfer matrix at roots of unity. The quantum-classical crossover is also discussed in terms of the eigenvalues of the Q-operator for a few special examples.