Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality
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arXiv
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| Format: | Preprint |
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2024
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| _version_ | 1866913382034046976 |
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| author | Chung, Jui-Hui Shapiro, Jacob |
| author_facet | Chung, Jui-Hui Shapiro, Jacob |
| contents | We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this abstract characterization, we define generalizations of this locality, which we term quasi-2D. We go on to calculate the path-connected components of spaces of unitaries or orthogonal projections which are quasi-2D-local and find a starkly different behavior compared with the actual 2D column of the Kitaev table, exhibiting e.g., in the unitary chiral case, infinitely many $\mathbb{Z}$-valued indices. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2406_05385 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality Chung, Jui-Hui Shapiro, Jacob Mathematical Physics Mesoscale and Nanoscale Physics Functional Analysis Quantum Physics We provide an alternative characterization of two-dimensional locality (necessary e.g. to define the Hall conductivity of a Fermi projection) using the spectral projections of the Laughlin flux operator. Using this abstract characterization, we define generalizations of this locality, which we term quasi-2D. We go on to calculate the path-connected components of spaces of unitaries or orthogonal projections which are quasi-2D-local and find a starkly different behavior compared with the actual 2D column of the Kitaev table, exhibiting e.g., in the unitary chiral case, infinitely many $\mathbb{Z}$-valued indices. |
| title | Topological Classification of Insulators: II. Quasi-Two-Dimensional Locality |
| topic | Mathematical Physics Mesoscale and Nanoscale Physics Functional Analysis Quantum Physics |
| url | https://arxiv.org/abs/2406.05385 |