论文标题
一维量子晶格模型中的二元性：拓扑领域
Dualities in one-dimensional quantum lattice models: topological sectors
论文作者
论文摘要
构建一个将双重理论的光谱构建一个通用框架是一个长期的开放问题。在这里，我们解决了具有对称扭曲边界条件的一维量子晶格模型的情况。在参考[PRX Quantum 4，020357]，在（绝对）对称模型之间定义了双重性，该模型仅在模块类别的选择中有所不同。使用矩阵产品运算符，我们从模块函子的数据中构造了显式对称性操作员，以保存边界条件以及互换二元模型的拓扑领域相互构建。我们用一个在旋转的双重类别中的示例家庭来说明我们的构建 - $ \ frac {1} {2} $ heisenberg xxz型号。一个模型的对称操作员形成融合类别$ \ mathsf {rep}（\ Mathcal S_3）$ \ Mathcal S_3 $的表示。我们发现，其拓扑扇区与XXZ模型的映射与$ \ Mathsf {Rep}（\ Mathcal S_3）$的Drinfel'd中心的非平凡编织自动等效性有关。
It has been a long-standing open problem to construct a general framework for relating the spectra of dual theories to each other. Here, we solve this problem for the case of one-dimensional quantum lattice models with symmetry-twisted boundary conditions. In ref. [PRX Quantum 4, 020357], dualities are defined between (categorically) symmetric models that only differ in a choice of module category. Using matrix product operators, we construct from the data of module functors explicit symmetry operators preserving boundary conditions as well as intertwiners mapping topological sectors of dual models onto one another. We illustrate our construction with a family of examples that are in the duality class of the spin-$\frac{1}{2}$ Heisenberg XXZ model. One model has symmetry operators forming the fusion category $\mathsf{Rep}(\mathcal S_3)$ of representations of the group $\mathcal S_3$. We find that the mapping between its topological sectors and those of the XXZ model is associated with the non-trivial braided auto-equivalence of the Drinfel'd center of $\mathsf{Rep}(\mathcal S_3)$.
