Emergent-gravity Hall effect from quantum geometry

Hiroki Yoshida; Takehito Yokoyama

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arXiv · 2507.18458

Emergent-gravity Hall effect from quantum geometry

Hiroki Yoshida·Takehito Yokoyama

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Abstract

We theoretically propose a Hall effect driven by effective gravitational fields arising from quantum geometry. We identify four mechanisms for this ``emergent-gravity Hall effect'': real-space gravity, momentum-space gravity, gravitational anomalous velocity, and gravitational Lorentz force, all of which are described by Christoffel symbols in real, momentum, or time spaces. Based on the semiclassical theory, we construct a unified theoretical framework to systematically investigate how emergent gravity in these spaces affects transport phenomena. We demonstrate these effects through model calculations and clarify the conditions under which a finite Hall response can arise. Our findings open a new avenue for exploring gravitational effects in quantum systems.

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cond-mat.other cond-mat.mes-hall cond-mat.str-el gr-qc quant-ph

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Hiroki Yoshida, Takehito Yokoyama. 2025-07-24. Emergent-gravity Hall effect from quantum geometry. https://arxiv.org/abs/2507.18458

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