AI 中文总结
本文解析研究二维SU(2)陈-西蒙斯物质理论描述的系统，分类其拓扑序与SET相，并计算耦合无质量物质场的SU(2)陈-西蒙斯理论的算子标度维数，为探索相关拓扑相提供指导。
AI 中文摘要
受最近数值研究中出现各种SU(2)陈-西蒙斯物质理论的启发，我们解析研究了由这类理论描述的二维系统中的拓扑相和量子临界性。首先，我们对具有p4×SO(3)对称性的所有格点自旋系统中的SU(2)k拓扑序进行分类，其中k为任意非零整数。我们发现，对于每个奇数k，该拓扑序可出现在具有任意Lieb-Schultz-Mattis（LSM）反常的系统中，且对称性无法对任意子进行置换。若系统具有非平凡（分别为平凡）LSM反常，则恰好存在1个（分别为9个）对称性增强拓扑（SET）相。另一方面，具有任意偶数k的SU(2)k拓扑序只能出现在具有平凡LSM反常的系统中。若k不属于{6,10,14,…}，则对称性无法对任意子进行置换，存在16个SET相；若k属于{6,10,14,…}，则对称性有4种不同的任意子置换方式，存在64个SET相。接下来，我们分析耦合Nf种无质量物质场（可为玻色子或费米子）的SU(2)k陈-西蒙斯理论。对于两种类型的理论，我们考虑Nf和k均很大且Nf/k固定的联合极限，并计算玻色子或费米子双线性算子的标度维数至1/Nf阶。这些结果加深了我们对这些涌现的奇异拓扑相和量子临界性的理解，并为进一步探索它们提供了有用指导。
英文摘要
Motivated by recent numerical studies where various $SU(2)$ Chern-Simons-matter theories emerge, we analytically study topological phases and quantum criticality in two-dimensional systems described by such theories. First, we classify $SU(2)_k$ topological orders in all lattice spin systems with a $p4\times SO(3)$ symmetry, where $k$ is an arbitrary nonzero integer. We find that for each odd $k$, the topological order can emerge in systems with an arbitrary Lieb-Schultz-Mattis (LSM) anomaly, and the symmetry cannot permute anyons. If the system has a nontrivial (respectively, trivial) LSM anomaly, then there is exactly one (respectively, nine) symmetry-enriched topological (SET) phases. On the other hand, $SU(2)_k$ topological order with any even $k$ can only emerge in systems with a trivial LSM anomaly. If $k\notin\{6, 10, 14, \cdots\}$, the symmetry cannot permute anyons, and there are 16 SET phases. If $k\in\{6, 10, 14, \cdots\}$, there are 4 different ways how the symmetry can permute anyons, and there are 64 SET phases. Next, we analyze the $SU(2)_k$ Chern-Simons theories coupled to $N_f$ flavors of gapless matter fields that can be either bosonic or fermionic. For both types of theories, we consider a joint large-$N_f$ and large-$k$ limit with $N_f/k$ fixed, and compute the scaling dimensions of the bilinear operators of the bosons or fermions to the order of $1/N_f$. These results sharpen our understanding of these emergent exotic topological phases and quantum criticality, and provide useful guidance to explore them further.
