Nonadiabatic Origin of Quantum-Metric Effects via Momentum-Space Metric Tensor
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866914419411255296 |
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| author | Ren, Yafei |
| author_facet | Ren, Yafei |
| contents | We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave packet theory to incorporate nonadiabatic effects, we introduce a momentum-space metric tensor -- the nonadiabatic metric. This metric gives rise to two velocity corrections, dubbed geometric and geodesic velocities, providing a unified and intuitive framework for understanding nonlinear and nonadiabatic transport phenomena beyond Berry phase effects. The geometric velocity is related to the nonadiabatic metric itself, whereas the geodesic velocity is a Christoffel symbol of the nonadiabatic metric. As the nonadiabatic metric is related to the energy-gap renormalized quantum metric, it unifies the broad quantum metric effects in electronic responses. When the nonadiabatic metric is constant, it reduces to an effective mass, modifying flat-band electron dynamics in confining potentials. In a flat Chern band with harmonic attractive interactions, the two-body wave functions mirror the Landau-level wave functions on a torus. Furthermore, we show that the nonadiabatic metric endows momentum space with a curved geometry, recasting wave packet dynamics as forced geodesic motion. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2506_06439 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Nonadiabatic Origin of Quantum-Metric Effects via Momentum-Space Metric Tensor Ren, Yafei Materials Science Mesoscale and Nanoscale Physics General Relativity and Quantum Cosmology We reveal a fundamental geometric structure of momentum space arising from the nonadiabatic evolution of Bloch electrons. By extending semiclassical wave packet theory to incorporate nonadiabatic effects, we introduce a momentum-space metric tensor -- the nonadiabatic metric. This metric gives rise to two velocity corrections, dubbed geometric and geodesic velocities, providing a unified and intuitive framework for understanding nonlinear and nonadiabatic transport phenomena beyond Berry phase effects. The geometric velocity is related to the nonadiabatic metric itself, whereas the geodesic velocity is a Christoffel symbol of the nonadiabatic metric. As the nonadiabatic metric is related to the energy-gap renormalized quantum metric, it unifies the broad quantum metric effects in electronic responses. When the nonadiabatic metric is constant, it reduces to an effective mass, modifying flat-band electron dynamics in confining potentials. In a flat Chern band with harmonic attractive interactions, the two-body wave functions mirror the Landau-level wave functions on a torus. Furthermore, we show that the nonadiabatic metric endows momentum space with a curved geometry, recasting wave packet dynamics as forced geodesic motion. |
| title | Nonadiabatic Origin of Quantum-Metric Effects via Momentum-Space Metric Tensor |
| topic | Materials Science Mesoscale and Nanoscale Physics General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2506.06439 |