发表机构
Princeton University; The Pennsylvania State University（普林斯顿大学; 宾夕法尼亚州立大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究针对具有U(1)⋊ℤ₂连续指数对称性的自旋链，明确其拓扑相由自旋S和基q决定，发现了超出现有分类的半SPT相等新型对称保护有隙相。
AI 中文摘要
我们研究具有连续指数对称性U(1)⋊ℤ₂（整数基为q）的一维自旋S链的对称有隙基态，其中U(1)电荷具有随格点j指数衰减的调制电荷单元q^(L−j)。最简单的模型是量子击穿模型，可视为XXZ Haldane自旋链的q-变形。我们证明，这些对称基态的拓扑结构关键取决于S和q：对于整数S，奇数q允许具有受保护边缘模的非平凡ℤ₂ Haldane型对称保护拓扑（SPT）相，而偶数q不允许非平凡SPT相；对于半整数S，奇数q因Lieb-Schultz-Mattis障碍禁止任何独特的对称有隙基态，而偶数q强制形成我们命名为“半SPT”相的新型对称有隙相。不同寻常的是，半SPT相仅在一个边缘具有对称保护的边缘模，且其弦序为SPT相的一半。我们的结果揭示了现有分类方案之外的新型对称保护有隙相。
英文摘要
We study symmetric gapped ground states of one-dimensional spin $S$ chains with a continuous exponential symmetry $U(1)\rtimes\mathbb Z_2$ with integer base $q$, where the U(1) charge has a modulated unit of charge $q^{L-j}$ decaying exponentially with site $j$. The simplest model is a quantum breakdown model that can be viewed as a $q$-deformation of the XXZ Haldane spin chain. We show that the topology of their symmetric ground states crucially depends on $S$ and $q$. For integer $S$, odd $q$ allows a nontrivial $\mathbb Z_2$ Haldane-type symmetry-protected topological (SPT) phase with protected edge modes, while even $q$ allows no nontrivial SPT phase. For half-odd integer $S$, odd $q$ prohibits any unique symmetric gapped ground state due to a Lieb-Schultz-Mattis obstruction, whereas even $q$ enforces a novel symmetric gapped phase which we name as the ``half-SPT" phase. Unconventionally, the half-SPT phase only has a symmetry protected edge mode on one edge, and has half of the string orders of an SPT phase. Our results uncover a new type of symmetry-protected gapped phases beyond existing classification schemes.
Comments6+2+2 pages
