论文标题
障碍物从不可变形的对称性造成的漏洞
Obstructions to Gapped Phases from Non-Invertible Symmetries
论文作者
论文摘要
3+1维中的量子系统在测量单一形式对称性下不变的量子系统享受由拓扑缺陷编码的新型非偶性对称性。这些对称性是限制动力学的重新归一化组不变性。我们表明，这种不可变形的对称性通常禁止具有间隙频谱的对称性真空状态。特别是，我们证明了一种具有$ \ mathbb {z} _ {n}^{（1）} $一形对称性的自我对齐理论是无处不在或自发地打破了自由度对称性，除非$ n = k^{2} {2} \ ell $ -1 $ -1 $ -1 $ -1 $ - $ -1 $ quadratic Modupue modulo $ \ Ell $ \ Ell $ \ Ell $。我们还将这些结果扩展到在更一般的测量操作下因不变性而引起的不可变形的对称性。试验对称性。一路上，我们发现对称性受保护的拓扑阶段中的二元性缺陷如何具有隐藏的时间反转对称性来组织其基本属性。这些不可变形的对称性是在晶格计的理论中实现的，这些理论可说明我们的结果。
Quantum systems in 3+1-dimensions that are invariant under gauging a one-form symmetry enjoy novel non-invertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain dynamics. We show that such non-invertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, we prove that a self-dual theory with $\mathbb{Z}_{N}^{(1)}$ one-form symmetry is gapless or spontaneously breaks the self-duality symmetry unless $N=k^{2}\ell$ where $-1$ is a quadratic residue modulo $\ell$. We also extend these results to non-invertible symmetries arising from invariance under more general gauging operations including e.g. triality symmetries. Along the way, we discover how duality defects in symmetry protected topological phases have a hidden time-reversal symmetry that organizes their basic properties. These non-invertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.
