Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866912196549672960 |
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| author | Paiva, Carolina Wang, Jie Ozawa, Tomoki Mera, Bruno |
| author_facet | Paiva, Carolina Wang, Jie Ozawa, Tomoki Mera, Bruno |
| contents | We present a new geometric characterization of generalized Landau levels (GLLs). The GLLs are a generalization of Landau levels to non-uniform Berry curvature, and are mathematically defined in terms of a holomorphic curve -- an ideal Kähler band -- and its associated unitary Frenet-Serret moving frame. Here, we find that GLLs are harmonic maps from the Brillouin zone to the complex projective space and they are critical points of the Dirichlet energy functional, as well as the static structure factor up to fourth order. We also find that filled GLLs exhibit quantized Hall viscosity, similar to the ordinary Landau levels. These results establish GLLs as a versatile generalization of Landau levels. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2501_11519 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity Paiva, Carolina Wang, Jie Ozawa, Tomoki Mera, Bruno Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics We present a new geometric characterization of generalized Landau levels (GLLs). The GLLs are a generalization of Landau levels to non-uniform Berry curvature, and are mathematically defined in terms of a holomorphic curve -- an ideal Kähler band -- and its associated unitary Frenet-Serret moving frame. Here, we find that GLLs are harmonic maps from the Brillouin zone to the complex projective space and they are critical points of the Dirichlet energy functional, as well as the static structure factor up to fourth order. We also find that filled GLLs exhibit quantized Hall viscosity, similar to the ordinary Landau levels. These results establish GLLs as a versatile generalization of Landau levels. |
| title | Geometrical Responses of Generalized Landau Levels: Structure Factor and the Quantized Hall Viscosity |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2501.11519 |