Geometric bound on structure factor

• URL: http://arxiv.org/abs/2412.02656v3
• Date: Mon, 28 Apr 2025 00:23:33 GMT
• Title: Geometric bound on structure factor
• Authors: Yugo Onishi, Alexander Avdoshkin, Liang Fu,
• Abstract summary: We show that a quadratic form of quantum geometric tensor in $k$-space sets a bound on the $q4$ term in the static structure factor $S(q)$ at small $vecq$.<n> Bands that saturate this bound satisfy a condition similar to Laplace's equation, leading us to refer to them as $textitharmonic bands$.
• Score: 44.99833362998488
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: 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.

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