发表机构
Department of Physics, the Pennsylvania State University; School of Physics and Astronomy, Shanghai Jiao Tong University（宾夕法尼亚州立大学物理系; 上海交通大学物理与天文学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对有隙系统量子相图，利用$S^1$-族的不可收缩性，结合奇异对称性相互作用推导新型拓扑分类，构建格点实现并验证其代数结构。
AI 中文摘要
我们通过识别间隙相图中环路（即所谓的$S^1$-族）的不可收缩性，研究了有隙系统量子相图的拓扑结构，其中多体哈密顿量可具有非平凡基态简并度。我们揭示了对称性在这类$S^1$-族分类中的作用，涉及奇异的对称性相互作用：（i）非平凡混合反常；（ii）自发破缺与未破缺对称性之间的半直积关系；（iii）具有不可逆算子的对称性。我们发现这类结构会产生基于“独立”对称性的早期分类无法实现的新型$S^1$-族分类。此外，我们构建了这些$S^1$-族的格点实现，并明确展示了其新型代数结构。
英文摘要
We study the topological structure of the quantum phase diagram of gapped systems by identifying the noncontractibility of loops, so-called $S^1$-families, within the gapped phase diagram in which many-body Hamiltonians can have nontrivial ground-state degeneracy. We manifest the role of symmetries in such $S^1$-family classifications by the exotic symmetry interplay: (i) nontrivial mixed anomalies, (ii) semi-direct product relation between the spontaneously broken and the unbroken symmetries, and (iii) symmetry with noninvertible operators. We find that such structures lead to the novel $S^1$-family classifications inaccessible by earlier classifications based on ``independent'' symmetries. Furthermore, we construct lattice realizations of these $S^1$-families and explicitly demonstrate their novel algebraic structures.
