Quantum Geometric Origin of Hall Viscosity and Nonlocal Hall Conductivity in Lattice Bands
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arXiv
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| Autori principali: | , , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866913164134711296 |
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| author | Shu, Danyu Sano, Ryotaro Yamakage, Ai Funaki, Hiroshi Matsuo, Mamoru |
| author_facet | Shu, Danyu Sano, Ryotaro Yamakage, Ai Funaki, Hiroshi Matsuo, Mamoru |
| contents | We show that Hall viscosity in lattice bands is governed by a band-projected electric quadrupole encoded within the quantum geometry: Berry curvature sets the projected-coordinate algebra, while the quantum metric determines the quadrupolar spread of a wave packet. The same structure enters the quadratic wave-vector coefficient of the nonlocal Hall conductivity, yielding a lattice viscosity-conductivity relation. In ideal bands, the deviation from the Landau-level form is quantified by Berry curvature fluctuations. Our results establish the nonlocal Hall response as an electrical signature of the quantum geometry underlying Hall viscosity and as a transport diagnostic of geometric idealness. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_27059 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quantum Geometric Origin of Hall Viscosity and Nonlocal Hall Conductivity in Lattice Bands Shu, Danyu Sano, Ryotaro Yamakage, Ai Funaki, Hiroshi Matsuo, Mamoru Mesoscale and Nanoscale Physics Strongly Correlated Electrons We show that Hall viscosity in lattice bands is governed by a band-projected electric quadrupole encoded within the quantum geometry: Berry curvature sets the projected-coordinate algebra, while the quantum metric determines the quadrupolar spread of a wave packet. The same structure enters the quadratic wave-vector coefficient of the nonlocal Hall conductivity, yielding a lattice viscosity-conductivity relation. In ideal bands, the deviation from the Landau-level form is quantified by Berry curvature fluctuations. Our results establish the nonlocal Hall response as an electrical signature of the quantum geometry underlying Hall viscosity and as a transport diagnostic of geometric idealness. |
| title | Quantum Geometric Origin of Hall Viscosity and Nonlocal Hall Conductivity in Lattice Bands |
| topic | Mesoscale and Nanoscale Physics Strongly Correlated Electrons |
| url | https://arxiv.org/abs/2605.27059 |