论文标题
各向异性较高等级$ \ mathbb {z} _n $拓扑阶段图
Anisotropic higher rank $\mathbb{Z}_N$ topological phases on graphs
论文作者
论文摘要
我们研究了异常的间隙拓扑阶段，在这些阶段中，他们接受$ \ mathbb {z} _n $分数激发，其方式与拓扑排序的阶段相同，但它们的基态退化取决于系统的局部几何形状。将这样的相放在由任意连接的图和1D线组成的2D晶格上，我们发现绘图激发的融合规则由图形的Laplacian描述，而超选择扇区的数量与Laplacian的核心有关。基于此分析，我们进一步表明，$ \ bigl [n \ times \ prod_ {i} \ text {gcd}（n，p_i）\ bigr]^2 $给出了基态堕落性，其中$ p_i $ $是laplacian的不变因素，是laplacian的不变因素，是一个比One and Gcd vers vers the Greats vers evers the evers evers the Greats vers evers the sever nive sever nive severs the spormes divisor。我们还讨论了准颗粒激发之间的编织统计数据。
We study unusual gapped topological phases where they admit $\mathbb{Z}_N$ fractional excitations in the same manner as topologically ordered phases, yet their ground state degeneracy depends on the local geometry of the system. Placing such phases on 2D lattice, composed of an arbitrary connected graph and 1D line, we find that the fusion rules of quasiparticle excitations are described by the Laplacian of the graph and that the number of superselection sectors is related to the kernel of the Laplacian. Based on this analysis, we further show that the ground state degeneracy is given by $\bigl[N\times \prod_{i}\text{gcd}(N, p_i)\bigr]^2$, where $p_i$'s are invariant factors of the Laplacian that are greater than one and gcd stands for the greatest common divisor. We also discuss braiding statistics between quasiparticle excitations.
