Quantum Many-Body Topology of Quasicrystals
Quantum Many-Body Topology of Quasicrystals
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DOI：
10.1103/physrevx.11.041051
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发表时间：
2021-03
影响因子：
12.5
通讯作者：
D. Else;Shengxun Huang;Abhinav Prem;A. Gromov
中科院分区：
文献类型：
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作者：
D. Else;Shengxun Huang;Abhinav Prem;A. Gromov
在本文中，我们描述了物质的准晶相互作用的拓扑相，即受某种准晶结构保护的相。我们证明了准晶体的弹性理论，它同时考虑了“声子”和“相子”模式，承认非平凡的量化拓扑项，其结构比它们的晶体对应物丰富得多。我们表明，这些术语对应于物质的不同相，也揭示了本质上的准晶相，没有晶体类似物。对于具有内部U(1)对称性的准晶体，我们讨论了一些拓扑项的解释和物理含义，包括d = 2准晶体中位错迁移率的约束和lieb - schultz - mattis - oshikaawa - hastings定理的准晶体推广。然后，我们进一步扩展了这些思想，并讨论了准晶拓扑相的完整分类，包括具有点群对称和不可逆相的系统。因此，我们得到了“准晶等效原理”，它将晶体拓扑相的分类推广到准晶设置。
In this paper, we characterize quasicrystalline interacting topological phases of matter i.e., phases protected by some quasicrystalline structure. We show that the elasticity theory of quasicrystals, which accounts for both “phonon” and “phason” modes, admits non-trivial quantized topological terms with far richer structure than their crystalline counterparts. We show that these terms correspond to distinct phases of matter and also uncover intrinsically quasicrystalline phases, which have no crystalline analogues. For quasicrystals with internal U(1) symmetry, we discuss a number of interpretations and physical implications of the topological terms, including constraints on the mobility of dislocations in d = 2 quasicrystals and a quasicrystalline generalization of the Lieb-Schultz-Mattis-Oshikawa-Hastings theorem. We then extend these ideas much further and address the complete classification of quasicrystalline topological phases, including systems with point-group symmetry as well as non-invertible phases. We hence obtain the “Quasicrystalline Equivalence Principle,” which generalizes the classification of crystalline topological phases to the quasicrystalline setting.