论文标题
确定无限投影纠缠状态的非亚伯拓扑顺序
Determining non-Abelian topological order from infinite projected entangled pair states
论文作者
论文摘要
我们概括了物理中引入的方法。 Rev. B 101，041108（2020）从与无限的预测纠缠对状态（IPEPS）代表的密切相关的二维系统的基础状态中提取有关拓扑顺序的信息。当包裹在圆环上时，独特的IPEP将变成堕落和局部无法区分的基础状态的叠加。我们发现IPEP的数值对称性，由无限矩阵产品运营商（MPO）及其融合规则表示。这些规则告诉我们如何将对称性结合到具有良好定义的任何磁通状态的状态中。 MPO投影仪的线性结构允许为每个状态有效地确定其第二个Renyi拓扑纠缠的熵，直接在无限长的圆柱体上，直接在无限缸宽度的极限下。相同的投影仪用于计算拓扑$ s $和$ t $矩阵编码紧急的人的共同统计数据。该算法由斐波那契和非亚伯弦网模型的示例说明。
We generalize the method introduced in Phys. Rev. B 101, 041108 (2020) of extracting information about topological order from the ground state of a strongly correlated two-dimensional system represented by an infinite projected entangled pair state (iPEPS) to non-Abelian topological order. When wrapped on a torus the unique iPEPS becomes a superposition of degenerate and locally indistinguishable ground states. We find numerically symmetries of the iPEPS, represented by infinite matrix product operators (MPO), and their fusion rules. The rules tell us how to combine the symmetries into projectors onto states with well defined anyon flux. A linear structure of the MPO projectors allows for efficient determination for each state its second Renyi topological entanglement entropy on an infinitely long cylinder directly in the limit of infinite cylinder's width. The same projectors are used to compute topological $S$ and $T$ matrices encoding mutual- and self-statistics of emergent anyons. The algorithm is illustrated by examples of Fibonacci and Ising non-Abelian string net models.
