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| Main Authors: | , , |
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| Format: | Preprint |
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2024
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2412.02656 |
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| _version_ | 1866916871797735424 |
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| author | Onishi, Yugo Avdoshkin, Alexander Fu, Liang |
| author_facet | Onishi, Yugo Avdoshkin, Alexander Fu, Liang |
| contents | We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q^4$ term in the static structure factor $S(q)$ at small $\vec{q}$. Bands that saturate this bound satisfy a condition similar to Laplace's equation, leading us to refer to them as $\textit{harmonic bands}$. We provide examples of harmonic bands in one- and two-dimensional systems, including (higher) Landau levels. The geometric bound further leads to a topological bound on the $q^4$ term, which is saturated only when the band geometry satisfies the trace condition and, additionally, the quantum geometric tensor is uniform in $k$-space. We speculate that these bounds taken together provide a useful guide for identifying Chern bands that favor (Abelian or non-Abelian) fractional Chern insulators. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2412_02656 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Geometric bound on structure factor Onishi, Yugo Avdoshkin, Alexander Fu, Liang Mesoscale and Nanoscale Physics Quantum Physics We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q^4$ term in the static structure factor $S(q)$ at small $\vec{q}$. Bands that saturate this bound satisfy a condition similar to Laplace's equation, leading us to refer to them as $\textit{harmonic bands}$. We provide examples of harmonic bands in one- and two-dimensional systems, including (higher) Landau levels. The geometric bound further leads to a topological bound on the $q^4$ term, which is saturated only when the band geometry satisfies the trace condition and, additionally, the quantum geometric tensor is uniform in $k$-space. We speculate that these bounds taken together provide a useful guide for identifying Chern bands that favor (Abelian or non-Abelian) fractional Chern insulators. |
| title | Geometric bound on structure factor |
| topic | Mesoscale and Nanoscale Physics Quantum Physics |
| url | https://arxiv.org/abs/2412.02656 |