发表机构
Key Laboratory of Quantum Materials and Devices of Ministry of Education, School of Physics, Southeast University; Department of Physics and Astronomy, University of British Columbia（东南大学物理学院教育部量子材料与器件重点实验室; 不列颠哥伦比亚大学物理与天文系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
该研究将涌现对称性思想应用于构造 Bott 时钟中费米子类拓扑量子临界点的全息表示，通过加倍自由度构造扩大对称性的晶格模型，其边界具有对应 tQCP 的红外动力学。
AI 中文摘要
在本文中，我们将涌现对称性的思想应用于构造 Bott 时钟中费米子类出现的一大类拓扑量子临界点（tQCPs）的全息表示。我们明确证明，在 Bott 时钟周围，d 维空间中具有保护对称性 Gp 的不同对称性保护的有隙相之间的 tQCP 处存在涌现对称性 U_EM。该涌现对称性可用于构造具有适当升级对称性的 (d+1) 维空间晶格模型，例如 U_EM×G_p 或 U_EM ⋊ G_p 等。通过加倍 d 维相邻拓扑类的自由度，我们成功证明，以此方式构造的 (d+1) 维晶格模型具有所需的扩大对称性群，这些对称性群恰好属于 Bott 时钟中逆时针方向的相邻拓扑类。此外，这些有隙拓扑类的 (d+1) 维晶格模型的 d 维边界表现出与 Bott 时钟中 d 维相邻拓扑相内相应 tQCP 相同的红外动力学，且对称性更低。
英文摘要
In this article, we apply the idea of emergent symmetries to construct holographic representations of a broad class of topological quantum critical points (tQCPs) that appear in fermionic classes in the Bott clock. We show explicitly that around the Bott clock, an emergent symmetry $U_{EM}$ exists at a tQCP between different symmetry protected gapped phases with protecting symmetry $G_p$ in $d$ spatial dimensions. This emergent symmetry can be used to construct a $(d+1)$ spatial dimensional lattice model with a properly upgraded symmetry such as $U_{EM}\times G_p$ or $U_{EM} \rtimes G_p$, etc. By doubling the degrees of freedom of the adjacent topological class in $d$-dimensions, we successfully show that the $(d+1)$-dimensional lattice models constructed in this way have the desired enlarged symmetry groups that precisely belong to the adjacent topological classes, counterclockwise around the Bott clock. Furthermore, $d$-dimensional boundaries of these $(d+1)$ dimensional lattice models of gapped topological classes are shown to exhibit identical infrared dynamics as the corresponding tQCPs in the $d$-dimensional adjacent topological phases in the Bott clock, with lower symmetries.
Comments13 pages, 3 figs, 1 table
