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arxiv: 2507.18458 · v2 · pith:SS5XIWDJnew · submitted 2025-07-24 · ❄️ cond-mat.other · cond-mat.mes-hall· cond-mat.str-el· gr-qc· quant-ph

Emergent-gravity Hall effect from quantum geometry

classification ❄️ cond-mat.other cond-mat.mes-hallcond-mat.str-elgr-qcquant-ph
keywords gravitationalhalleffectgravityquantumeffectsemergent-gravitygeometry
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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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