论文标题
$ z_3 $和$（\ times z_3）^3 $对称受保护的拓扑标准
$Z_3$ and $(\times Z_3)^3$ symmetry protected topological paramagnets
论文作者
论文摘要
我们在由$（\ times z_3）^3 \ equiv z_3 \ times z_3 \ times z_3 $ symmetry和较小的$ z_3 $对称性的三角形晶格上识别具有空隙边缘模式的二维三态PARAMAGNETS，具有空隙边缘模式。我们得出了无间隙边缘的微观模型，揭示了它们的对称性并分析了共形性能。我们通过采用数值密度 - 矩阵重新归一化组（DMRG）模拟和精确的对角线化来研究无间隙边缘的性质。我们讨论相应的保形场理论，其中心电荷和相应主要场的缩放维度。我们认为，边缘模式的低能限制是由$ su_k（3）/su_k（2）$ coset共形场理论，其级别$ k = 2 $。讨论的二维模型实现了各种受对称性保护的拓扑阶段，为研究它们之间非常规量子关键的研究打开了一个窗口。
We identify two-dimensional three-state Potts paramagnets with gapless edge modes on a triangular lattice protected by $(\times Z_3)^3\equiv Z_3\times Z_3\times Z_3$ symmetry and smaller $Z_3$ symmetry. We derive microscopic models for the gapless edge, uncover their symmetries, and analyze the conformal properties. We study the properties of the gapless edge by employing the numerical density-matrix renormalization group (DMRG) simulation and exact diagonalization. We discuss the corresponding conformal field theory, its central charge, and the scaling dimension of the corresponding primary field. We argue that the low energy limit of our edge modes is defined by the $SU_k(3)/SU_k(2)$ coset conformal field theory with the level $k=2$. The discussed two-dimensional models realize a variety of symmetry-protected topological phases, opening a window for studies of the unconventional quantum criticalities between them.
