Quantum geometry, Structure factor, and Topological bounds
ORAL · Invited
Abstract
Topological materials exhibit distinctive physical properties rooted in the topology of the electronic Bloch wave functions. In recent years, the quantum metric, a measure of the distance between quantum states, has attracted growing attention to characterize these wave functions. Together with the Berry curvature, it defines quantum geometry of electronic states, providing a unified geometric framework that complements the topological concepts.
In this talk, I will discuss how quantum geometry leads to universal bounds of physical quantities in topological materials — topological bounds. Specifically, I will demonstrate that the static structure factor is directly related to quantum geometry [1] and obeys universal bounds determined by a topological invariant, Chern number [2]. This relation yields a fundamental topological bound on the energy gap of Chern insulators [3]. Remarkably, these results remain exact even in interacting systems, such as fractional Chern insulators. Through these topological bounds, I will illustrate how quantum geometry reveals new and universal aspects of topological phases.
[1] Y. Onishi and L. Fu, Quantum weight: A fundamental property of quantum many-body systems, Phys. Rev. Res. 7, 023158 (2025).
[2] Y. Onishi and L. Fu, Topological Bound on the Structure Factor, Phys. Rev. Lett. 133, 206602 (2024).
[3] Y. Onishi and L. Fu, Fundamental Bound on Topological Gap, Phys. Rev. X 14, 011052 (2024).
In this talk, I will discuss how quantum geometry leads to universal bounds of physical quantities in topological materials — topological bounds. Specifically, I will demonstrate that the static structure factor is directly related to quantum geometry [1] and obeys universal bounds determined by a topological invariant, Chern number [2]. This relation yields a fundamental topological bound on the energy gap of Chern insulators [3]. Remarkably, these results remain exact even in interacting systems, such as fractional Chern insulators. Through these topological bounds, I will illustrate how quantum geometry reveals new and universal aspects of topological phases.
[1] Y. Onishi and L. Fu, Quantum weight: A fundamental property of quantum many-body systems, Phys. Rev. Res. 7, 023158 (2025).
[2] Y. Onishi and L. Fu, Topological Bound on the Structure Factor, Phys. Rev. Lett. 133, 206602 (2024).
[3] Y. Onishi and L. Fu, Fundamental Bound on Topological Gap, Phys. Rev. X 14, 011052 (2024).
*This work was supported by National Science Foundation (NSF) Convergence Accelerator Award No. 2235945, the U.S. Army Research Laboratory and the U.S. Army Research Office through the Institute for Soldier Nanotechnologies under Collaborative Agreement No. W911NF-18-2-0048, and a Simons Investigator Award from the Simons Foundation.
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Publication: [1] Y. Onishi and L. Fu, Quantum weight: A fundamental property of quantum many-body systems, Phys. Rev. Res. 7, 023158 (2025).
[2] Y. Onishi and L. Fu, Topological Bound on the Structure Factor, Phys. Rev. Lett. 133, 206602 (2024).
[3] Y. Onishi and L. Fu, Fundamental Bound on Topological Gap, Phys. Rev. X 14, 011052 (2024).
Presenters
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Yugo Onishi
- Massachusetts Institute of Technology