Topological Equivalence between the Fibonacci Quasicrystal and the Harper Model
Open accessAbstract
One-dimensional quasiperiodic systems, such as the Harper model and the Fibonacci quasicrystal, have long been the focus of extensive theoretical and experimental research. Recently, the Harper model was found to be topologically nontrivial. Here, we derive a general model that embodies a continuous deformation between these seemingly unrelated models. We show that this deformation does not close any bulk gaps, and thus prove that these models are in fact topologically equivalent. Remarkably, they are equivalent regardless of whether the quasiperiodicity appears as an on-site or hopping modulation. This proves that these different models share the same boundary phenomena and explains past measurements. We generalize this equivalence to any Fibonacci-like quasicrystal, i.e., a cut and project in any irrational angle.
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The diffraction of light through the array mimics the time-evolution of the wavefunction of a quantum mechanical particle.
“Therefore, the diffraction of light through the array mimics the timeevolution of the wavefunction of a quantum mechanical particle 36-38 .”
From Photonic topological boundary pumping as a probe of 4D quantum Hall physics (2018) · cites this paper as [37]
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References 30 · Cited by 298
- Authors
- Kraus, Y. E., & Zilberberg, O.
- Affiliations
- Weizmann Institute of Science (IL)
- ORCID
- Zilberberg, Oded
- Venue
- Physical Review Letters
- Publisher
- American Physical Society (APS)
- Published
- 2012-09-13
- Volume
- 109
- Issue
- 11
- Pages
- 116404-116404
- ISSN
- 0031-9007 (ISSN-L)
- 1079-7114
- OpenAlex
- W2071515958
- Cited by
- 298
- References
- 30
- Citations by year
- 2026: 23 · 2025: 19 · 2024: 30 · 2023: 23 · 2022: 35 · 2021: 35 · 2020: 19 · 2019: 24 · 2018: 22 · 2017: 15 · 2016: 10 · 2015: 21 · 2014: 14 · 2013: 8
- FWCI
- 7.12
- Type
- journal article
- Language
- en
- Open access
- green
- arxiv.org
- Locations
- Physical Review Letters (publishedVersion)
- PubMed (publishedVersion)
- arXiv (Cornell University) (submittedVersion)
- arXiv (Cornell University)
- Topics
- Physical Sciences › Physics and Astronomy › Atomic and Molecular Physics, and Optics › Topological Materials and Phenomena
- Physical Sciences › Materials Science › Materials Chemistry › Quasicrystal Structures and Properties
- Physical Sciences › Mathematics › Mathematical Physics › Spectral Theory in Mathematical Physics
- Keywords
- topological equivalence, Fibonacci quasicrystals, Harper model, quasiperiodic systems, topological invariants, continuous deformation, boundary states, cut-and-project sets, irrational rotation
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