论文标题
矩阵量子组作为lie组的矩阵产品操作员表示
Matrix quantum groups as matrix product operator representations of Lie groups
论文作者
论文摘要
我们证明，矩阵量子组$ sl_q（2）$产生了Lie Group $ SL（2）$的非平凡矩阵产品操作员表示，提供了XXZ模型的非平凡全局$ SU（2）$对称性的明确表征。矩阵产品运算符是非注射剂，其集合在乘法下关闭。这允许计算作用于虚拟或量子自由度的融合量，并获得满足五角大楼关系的重新耦合系数。我们认为，这些数据与众所周知的$ q $ od-q $ qubsch-gordan系数和6J符号的组合与对BiModule类别的量子组的描述一致。
We demonstrate that the matrix quantum group $SL_q(2)$ gives rise to nontrivial matrix product operator representations of the Lie group $SL(2)$, providing an explicit characterization of the nontrivial global $SU(2)$ symmetry of the XXZ model with periodic boundary conditions. The matrix product operators are non-injective and their set is closed under multiplication. This allows to calculate the fusion tensors acting on the virtual or quantum degrees of freedom and to obtain the recoupling coefficients, which satisfy a type of pentagon relation. We argue that the combination of this data with the well known $q$-deformed Clebsch-Gordan coefficients and 6j-symbols is consistent with a description of this quantum group in terms of bimodule categories.
