Dual Symmetry Classification of Non-Hermitian Systems and $\mathbb{Z}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866913381759320064 |
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| author | Jiang, Zhiyu Okamoto, Ryo Obuse, Hideaki |
| author_facet | Jiang, Zhiyu Okamoto, Ryo Obuse, Hideaki |
| contents | Non-Hermitian systems exhibit richer topological properties compared to their Hermitian counterparts. It is well known that non-Hermitian systems have been classified based on either the symmetry relations for non-Hermitian Hamiltonians or the symmetry relations for non-unitary time-evolution operators in the context of Floquet topological phases. In this work, we propose that non-Hermitian systems can always be classified in two ways; a non-Hermitian system can be classified using the symmetry relations for non-Hermitian Hamiltonians or time-evolution operator regardless of the Floquet topological phases or not. We refer to this as dual symmetry classification. To demonstrate this, we successfully introduce a new non-unitary quantum walk that exhibits point gaps with a $\mathbb{Z}_2$ point-gap topological phase applying the dual symmetry classification and treating the time-evolution operator of this quantum walk as the non-Hermitian Hamiltonian. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_04147 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dual Symmetry Classification of Non-Hermitian Systems and $\mathbb{Z}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk Jiang, Zhiyu Okamoto, Ryo Obuse, Hideaki Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics Non-Hermitian systems exhibit richer topological properties compared to their Hermitian counterparts. It is well known that non-Hermitian systems have been classified based on either the symmetry relations for non-Hermitian Hamiltonians or the symmetry relations for non-unitary time-evolution operators in the context of Floquet topological phases. In this work, we propose that non-Hermitian systems can always be classified in two ways; a non-Hermitian system can be classified using the symmetry relations for non-Hermitian Hamiltonians or time-evolution operator regardless of the Floquet topological phases or not. We refer to this as dual symmetry classification. To demonstrate this, we successfully introduce a new non-unitary quantum walk that exhibits point gaps with a $\mathbb{Z}_2$ point-gap topological phase applying the dual symmetry classification and treating the time-evolution operator of this quantum walk as the non-Hermitian Hamiltonian. |
| title | Dual Symmetry Classification of Non-Hermitian Systems and $\mathbb{Z}_2$ Point-Gap Topology of a Non-Unitary Quantum Walk |
| topic | Mesoscale and Nanoscale Physics Statistical Mechanics Quantum Physics |
| url | https://arxiv.org/abs/2403.04147 |