表面拓扑序和一种新的相互作用t Hooft反常使能3+ 1维费米子SPT
Surface Topological Order and a new 't Hooft Anomaly of Interaction Enabled 3+1D Fermion SPTs
摘要：
对称性保护拓扑（SPT）相在自由费米子和相互作用但本质上是玻色子模型的背景下得到了很好的理解。最近人们认识到，存在只出现在相互作用模型中的本征费米子SPT。在这里，我们表明，这些阶段的3+1维实现具有表面状态的特点是一个新的't Hooft异常，捕获的$H^3(G, Z_2)$类。这被编码在具有拓扑序的表面态上的对称性的反常作用中，这必然会置换任意子。我们详细讨论了对称群$G = Z_2 \times Z_4$的一个例子。使用网络模型的表面，我们推导出一个候选的表面拓扑秩序的$Z_4$规范理论。我们将我们的研究结果异常值$H^3$与各种系数先前介绍的玻色子和费米子设置，并描述了一个通用的框架，统一这些各种异常。
英文摘要：
Symmetry protected topological (SPT) phases are well understood in the context of free fermions and in the context of interacting but essentially bosonic models. Recently it has been realized that intrinsically fermionic SPTs exist which only appear in interacting models. Here we show that the 3+1 dimensional realizations of these phases have surface states characterized by a new 't Hooft anomaly, captured by a $H^3(G, Z_2)$ class. This is encoded in the anomalous action of symmetry on the surface states with topological order, which must necessarily permute the anyons. We discuss in detail an example with symmetry group $G = Z_2 \times Z_4$. Using a network model of the surface we derive a candidate surface topological order given by a $Z_4$ gauge theory. We relate our findings to anomalies valued in $H^3$ with various coefficients introduced previously in both bosonic and fermionic settings, and describe a general framework that unifies these various anomalies.
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