Homotopy of periodic two by two matrices
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929248884752384 |
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| author | Avron, Joseph E. Turner, Ari M. |
| author_facet | Avron, Joseph E. Turner, Ari M. |
| contents | We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped Bloch Hamiltonians in 1D with a two-dimensional Hilbert space per unit cell. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_07529 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Homotopy of periodic two by two matrices Avron, Joseph E. Turner, Ari M. Mathematical Physics We describe the homotopy classes of 2 by 2 periodic simple (=non-degenerate) matrices with various symmetries. This turns out to be an elementary exercise in the homotopy of closed curves in three dimensions. The matrices represent gapped Bloch Hamiltonians in 1D with a two-dimensional Hilbert space per unit cell. |
| title | Homotopy of periodic two by two matrices |
| topic | Mathematical Physics |
| url | https://arxiv.org/abs/2212.07529 |