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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2401.12674 |
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| _version_ | 1866916103362445312 |
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| author | Nakamura, Masaaki Masuda, Shohei |
| author_facet | Nakamura, Masaaki Masuda, Shohei |
| contents | We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of Fukui-Hatsugai-Suzuki's method, based on lattice gauge theory, and the Coh-Vanderbilt's method, which relates to electronic polarization. The essential point of this discussion is that the insertion of flux into the extended one-dimensional chain generates an effective current in the perpendicular direction. These methods are valuable not only for a unified understanding of topological physics in different dimensions but also for numerical calculations, including the density matrix renormalization group. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2401_12674 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Chern numbers in two-dimensional systems with spiral boundary conditions Nakamura, Masaaki Masuda, Shohei Strongly Correlated Electrons We discuss methods for calculating Chern numbers of two-dimensional lattice systems using spiral boundary conditions, which sweep all lattice sites in one-dimensional order. Specifically, we establish the one-dimensional representation of Fukui-Hatsugai-Suzuki's method, based on lattice gauge theory, and the Coh-Vanderbilt's method, which relates to electronic polarization. The essential point of this discussion is that the insertion of flux into the extended one-dimensional chain generates an effective current in the perpendicular direction. These methods are valuable not only for a unified understanding of topological physics in different dimensions but also for numerical calculations, including the density matrix renormalization group. |
| title | Chern numbers in two-dimensional systems with spiral boundary conditions |
| topic | Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2401.12674 |