发表机构
The University of Tokyo; University of Oxford; Kyoto University（东京大学; 牛津大学; 京都大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文研究非在位对称性保护的可逆相，发现晶格反常可移动可逆相集合，构造$p+ip$超导体的$\mathbb Z_4^F$对称性，将允许的$c_-$从整数移至半整数，并推广至$U(1)^f$对称性，为研究新可逆相提供方向。
AI 中文摘要
我们研究了由携带非平凡晶格反常指标的非在位对称性所保护的可逆相。虽然晶格反常通常被视为对称短程纠缠（SRE）态的障碍，但我们表明，反常晶格对称性仍然可以容许不是SRE的可逆相，并且还可以移动对称兼容的可逆相的集合。特别地，我们考虑了（2+1）维中的费米子$\mathbb Z_4^F$对称性。对于在位$\mathbb Z_4^F$对称性，对称可逆相具有整数手征中心荷$c_-\in\mathbb Z$，而具有非平凡晶格反常指标的非在位对称性尽管具有平凡的连续体't Hooft反常，却阻碍了所有这样的相。我们通过构造一个具有$c_-=1/2$的$p+ip$超导体的精确指数准局域$\mathbb Z_4^F$对称性来解决这个问题。我们计算了它的晶格反常，并发现该对称性确实禁止了$c_-\in \mathbb{Z}$的可逆态。因此，允许的可逆相被移动到$c_-\in\mathbb Z+1/2$。通过规范$p+ip$超导体的费米子奇偶性，可以获得由$\mathbb Z_4$对称性丰富的伊辛拓扑序。我们用融合2-范畴描述了相应的对称结构。我们进一步表明，$p+ip$态容许一个扩展的非在位$U(1)^f$对称性，提供了可逆相中分数量子霍尔响应的类似物。这种非在位$U(1)^f$对称性再次禁止携带$c_-\in\mathbb{Z}$的陈绝缘体，而与$c_-\in\mathbb{Z}+1/2$的可逆态兼容。这一结果促进了对由非在位对称性丰富的新的可逆相和自旋液体类别的系统研究。
英文摘要
We study invertible phases protected by non-onsite symmetries carrying nontrivial lattice anomaly indices. While lattice anomalies are usually viewed as obstructions to symmetric short-range-entangled (SRE) states, we show that anomalous lattice symmetries can nevertheless admit invertible phases that are not SRE, and can moreover shift the set of symmetry-compatible invertible phases. In particular, we consider a fermionic $\mathbb Z_4^F$ symmetry in (2+1) dimensions. For an onsite $\mathbb Z_4^F$ symmetry, symmetric invertible phases have integer chiral central charge $c_-\in\mathbb Z$, whereas a non-onsite symmetry with nontrivial lattice anomaly index obstructs all such phases despite having trivial continuum 't Hooft anomaly. We resolve this by constructing an exact exponentially quasi-local $\mathbb Z_4^F$ symmetry of a $p+ip$ superconductor with $c_-=1/2$. We compute its lattice anomaly, and find that the symmetry indeed forbids $c_-\in \mathbb{Z}$ invertible states. The allowed invertible phases are consequently shifted to $c_-\in\mathbb Z+1/2$. By gauging the fermion parity of the $p+ip$ superconductor, one obtains an Ising topological order enriched by a $\mathbb Z_4$ symmetry. We describe the corresponding symmetry structure in terms of a fusion 2-category. We further show that the $p+ip$ state admits an enlarged non-onsite $U(1)^f$ symmetry, providing an analogue of fractional quantum Hall response in an invertible phase. This non-onsite $U(1)^f$ symmetry again forbids Chern insulators carrying $c_-\in\mathbb{Z}$, while being compatible with invertible states with $c_-\in\mathbb{Z}+1/2$. This result motivates a systematic study of new classes of invertible phases and spin liquids enriched by non-onsite symmetries.
Comments16 pages
