Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence"
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| Format: | Preprint |
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2023
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| _version_ | 1866910468333895680 |
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| author | Slager, Robert-Jan Bouhon, Adrien Ünal, F. Nur |
| author_facet | Slager, Robert-Jan Bouhon, Adrien Ünal, F. Nur |
| contents | We comment on the recent paper ``Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm. {\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to study multi-gap topology in Floquet systems for the first time, only known homotopic relations are presented. While such insights are used to present interesting Floquet phenomena and phases, which is an attractive result in itself, they cannot be used to deduce the total bulk characterization in the dynamical context without further proof. In fact, the authors essentially rephrase a Zak phase description. These results should in particular be contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak phases {\it and} dynamical Dirac strings were shown to be able to {\it distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional systems. As a result, the claim of a sharp multifold bulk-edge correspondence cannot be concluded from the given arguments. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2310_12782 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" Slager, Robert-Jan Bouhon, Adrien Ünal, F. Nur Mesoscale and Nanoscale Physics Materials Science Quantum Gases Mathematical Physics Quantum Physics We comment on the recent paper ``Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" by Tianyu Li and Haiping Hu, Nat. Comm. {\bf 14}, 6418 (2023). Apart from the fact that the authors unjustly imply to study multi-gap topology in Floquet systems for the first time, only known homotopic relations are presented. While such insights are used to present interesting Floquet phenomena and phases, which is an attractive result in itself, they cannot be used to deduce the total bulk characterization in the dynamical context without further proof. In fact, the authors essentially rephrase a Zak phase description. These results should in particular be contrasted to earlier results, arXiv:2208.12824, in which static-compatible Zak phases {\it and} dynamical Dirac strings were shown to be able to {\it distinguish} rather similar non-Abelian Floquet phases in $2+1$ dimensional systems. As a result, the claim of a sharp multifold bulk-edge correspondence cannot be concluded from the given arguments. |
| title | Comment on "Floquet non-Abelian topological insulator and multifold bulk-edge correspondence" |
| topic | Mesoscale and Nanoscale Physics Materials Science Quantum Gases Mathematical Physics Quantum Physics |
| url | https://arxiv.org/abs/2310.12782 |