Emergent-gravity Hall effect from quantum geometry
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866909706136584192 |
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| author | Yoshida, Hiroki Yokoyama, Takehito |
| author_facet | Yoshida, Hiroki Yokoyama, Takehito |
| contents | We theoretically propose a Hall effect driven by effective gravitational fields arising from quantum geometry. We develop four mechanisms for this ''emergent-gravity Hall effect" : real-space gravity, momentum-space gravity, gravitional anomalous velocity, and gravitational Lorentz force which are described by the Christoffel symbols in real, momentum, and time spaces. We construct a unified theoretical framework to systematically investigate the effects of emergent gravity in these spaces on transport phenomena based on the semiclassical theory. We demonstrate these effects by 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_18458 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Emergent-gravity Hall effect from quantum geometry Yoshida, Hiroki Yokoyama, Takehito Other Condensed Matter Mesoscale and Nanoscale Physics Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics We theoretically propose a Hall effect driven by effective gravitational fields arising from quantum geometry. We develop four mechanisms for this ''emergent-gravity Hall effect" : real-space gravity, momentum-space gravity, gravitional anomalous velocity, and gravitational Lorentz force which are described by the Christoffel symbols in real, momentum, and time spaces. We construct a unified theoretical framework to systematically investigate the effects of emergent gravity in these spaces on transport phenomena based on the semiclassical theory. We demonstrate these effects by 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. |
| title | Emergent-gravity Hall effect from quantum geometry |
| topic | Other Condensed Matter Mesoscale and Nanoscale Physics Strongly Correlated Electrons General Relativity and Quantum Cosmology Quantum Physics |
| url | https://arxiv.org/abs/2507.18458 |