论文标题
对称性和现场张量网络状态
Symmetries and field tensor network states
论文作者
论文摘要
我们研究张量张量张量网络状态（FTNS）的张量网络类别的物理和虚拟空间的对称表示之间的相互作用。这些是通过构造无限尺寸张量网络的虚拟空间通过保形场理论（CFT）描述的。我们可以将物理索引上的对称性表示为换向器，并在虚拟空间上具有相应的CFT电流。到那时，我们可以研究该状态的临界对称性受保护的拓扑特性，类似于对矩阵乘积状态的对称性保护拓扑秩序的分类。我们使用它来分析得出Majumdar-Ghosh点的两个接地状态的临界对称性受保护的拓扑特性，相对于先前定义的对称性。
We study the interplay between symmetry representations of the physical and virtual space on the class of tensor network states for critical spins systems known as field tensor network states (fTNS). These are by construction infinite dimensional tensor networks whose virtual space is described by a conformal field theory (CFT). We can represent a symmetry on the physical index as a commutator with the corresponding CFT current on the virtual space. By then studying this virtual space representation we can learn about the critical symmetry protected topological properties of the state, akin to the classification of symmetry protected topological order for matrix product states. We use this to analytically derive the critical symmetry protected topological properties of the two ground states of the Majumdar-Ghosh point with respect to the previously defined symmetries.
