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Quantum Many-Body Topology of Quasicrystals

TitleQuantum Many-Body Topology of Quasicrystals
Publication TypeJournal Article
Year of Publication2021
Authors, S-J. Huang, A. Prem, and A. Gromov
JournalPhys. Rev. X
Volume11
Date PublishedDEC 14
Type of ArticleArticle
ISSN2160-3308
Abstract

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 nontrivial 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 analogs. 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 noninvertible phases. We hence obtain the ``quasicrystalline equivalence principle,{''} which generalizes the classification of crystalline topological phases to the quasicrystalline setting.

DOI10.1103/PhysRevX.11.041051