Title: Anomalies of Coset Non-Invertible Symmetries Show Chinese title

Title: 共轭非可逆对称性的异常

Abstract: Anomalies of global symmetries provide important information on the quantum dynamics. We show the dynamical constraints can be organized into three classes: genuine anomalies, fractional topological responses, and integer responses that can be realized in symmetry-protected topological (SPT) phases. Coset symmetry can be present in many physical systems including quantum spin liquids, and the coset symmetry can be a non-invertible symmetry. We introduce twists in coset symmetries, which modify the fusion rules and the generalized Frobenius-Schur indicators. We call such coset symmetries twisted coset symmetries, and they are labeled by the quadruple $(G,K,\omega_{D+1},\alpha_D)$ in $D$ spacetime dimensions where $G$ is a group and $K\subset G$ is a discrete subgroup, $\omega_{D+1}$ is a $(D+1)$-cocycle for group $G$, and $\alpha_{D}$ is a $D$-cochain for group $K$. We present several examples with twisted coset symmetries using lattice models and field theory, including both gapped and gapless systems (such as gapless symmetry-protected topological phases). We investigate the anomalies of general twisted coset symmetry, which presents obstructions to realizing the coset symmetry in (gapped) symmetry-protected topological phases. We show that finite coset symmetry $G/K$ becomes anomalous when $G$ cannot be expressed as the bicrossed product $G=H\Join K$, and such anomalous coset symmetry leads to symmetry-enforced gaplessness in generic spacetime dimensions. We illustrate examples of anomalous coset symmetries with $A_5/\mathbb{Z}_2$ symmetry, with realizations in lattice models. Show Chinese abstract

Abstract: 全局对称性的异常为量子动力学提供了重要的信息。 我们表明动力学约束可以分为三类：真实异常、分数拓扑响应以及可以在对称性保护的拓扑(SPT)相中实现的整数响应。 共轭对称性可以存在于许多物理系统中，包括量子自旋液体，并且共轭对称性可以是一种不可逆对称性。 我们引入了共轭对称性的扭变，这会修改融合规则和广义的弗罗贝尼乌斯-施瓦茨指标。 我们称这种陪集对称为扭曲陪集对称性，它们由四元组$(G,K,\omega_{D+1},\alpha_D)$标识，在$D$维时空其中$G$是一个群，$K\subset G$是一个离散子群，$\omega_{D+1}$是群$G$的$(D+1)$-上循环，而$\alpha_{D}$是群$K$的$D$-上链。 我们使用格点模型和场论展示了具有扭曲陪集对称性的几个例子，包括有能隙和无能隙系统（如无能隙对称性保护拓扑相）。 我们研究了普遍扭曲陪集对称性的反常，这会阻碍在（有能隙）对称性保护拓扑相中实现陪集对称性。 我们表明，当$G$无法表示为双交叉积$G=H\Join K$时，有限陪集对称性$G/K$会变得反常，并且这种反常的陪集对称性会导致通用时空维度中的对称性强制无能隙性。 我们用$A_5/\mathbb{Z}_2$对称性说明了反常陪集对称性的例子，并在格点模型中实现了这些例子。