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arXiv:2608.18347

Quantum-geometric bounds on Casimir repulsion

Adolfo G. Grushin

quant-phcond-mat.mes-hallSubmitted Aug 18, 2026• Announced Aug 20, 2026
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Abstract

The quantum geometric tensor has been shown to bound the gap, optical absorption, and dielectric susceptibilities of materials. Here we derive new quantum-geometric bounds on the magnitude and sign of the Casimir force between two-dimensional plates in the long-distance limit. These bounds limit the previously attributed benefit of increasing the plate's Chern number to maximize repulsion, and give a quantum geometric origin to the stronger attractive force of metallic plates, regardless of their Chern number. These bounds allow us to infer that flat Chern bands that saturate geometric bounds, including Landau levels and moiré flat bands, enlarge the window where Casimir repulsion exists and bring the repulsive crossover to smaller, more experimentally relevant distances. We derive estimates for material platforms such as twisted MoTe$_2$. Our work shows that quantum-geometric bounds constrain repulsive Casimir forces beyond previously known theorems, and suggests new optimization strategies to observe repulsion.

Comments
5+7 pages, 3+1 figures

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The quantum geometric tensor has been shown to bound the gap, optical absorption, and dielectric susceptibilities of materials. Here we derive new quantum-geometric bounds on the magnitude and sign of the Casimir force between two-dimensional plates in the long-distance limit. These bounds limit the previously attributed benefit of increasing the plate's Chern number to maximize repulsion, and give a quantum geometric origin to the stronger attractive force of metallic plates, regardless of their Chern number. These bounds allow us to infer that flat Chern bands that saturate geometric bounds, including Landau levels and moiré flat bands, enlarge the window where Casimir repulsion exists and bring the repulsive crossover to smaller, more experimentally relevant distances. We derive estimates for material platforms such as twisted MoTe2_22​. Our work shows that quantum-geometric bounds constrain repulsive Casimir forces beyond previously known theorems, and suggests new optimization strategies to observe repulsion.
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We show that quantum fluctuations of electromagnetic fields induce an extensive zero-point energy in insulators. The zero-point energy density is proportional to the quantum fluctuation of electric polarization in the many-body ground state, a fundamental quantum geometric property of solids known as the quantum weight. For fields produced by a superconducting LC circuit, the zero-point energy results in a repulsive force between the circuit and the material and an attractive force on the capacitor plates, which we call quantum geometric force. The force on the capacitor plates is proportional to the quantum weight, inversely proportional to the plate area, and independent of the plate distance. The proposed effects provide direct experimental access to the many-body quantum geometry and reveal a new quantum geometric effect in macroscopic solids induced by vacuum fluctuation.
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