Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations
This work provides a surprisingly simple demonstration that the quantized Hall conductivity of correlated insulators is given by the many-body Chern number, a topological invariant defined in the space of twisted boundary conditions. In contrast to conventional proofs, generally based on the Kubo fo...
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| Format: | Article |
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Académie des sciences
2024-09-01
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| Series: | Comptes Rendus. Physique |
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| Online Access: | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.191/ |
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| author | Goldman, Nathan Ozawa, Tomoki |
| author_facet | Goldman, Nathan Ozawa, Tomoki |
| author_sort | Goldman, Nathan |
| collection | DOAJ |
| description | This work provides a surprisingly simple demonstration that the quantized Hall conductivity of correlated insulators is given by the many-body Chern number, a topological invariant defined in the space of twisted boundary conditions. In contrast to conventional proofs, generally based on the Kubo formula, our approach entirely relies on combining Kramers–Kronig relations and Fermi’s golden rule within a circular-dichroism framework. This pedagogical derivation illustrates how the Hall conductivity of correlated insulators can be determined by monitoring single-particle excitations upon a circular drive, a conceptually simple picture with direct implications for quantum-engineered systems, where excitation rates can be directly monitored. |
| format | Article |
| id | doaj-art-d9d48d75367c4162a98324b8008eb669 |
| institution | Kabale University |
| issn | 1878-1535 |
| language | English |
| publishDate | 2024-09-01 |
| publisher | Académie des sciences |
| record_format | Article |
| series | Comptes Rendus. Physique |
| spelling | doaj-art-d9d48d75367c4162a98324b8008eb6692025-02-07T13:53:46ZengAcadémie des sciencesComptes Rendus. Physique1878-15352024-09-0125G128930210.5802/crphys.19110.5802/crphys.191Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relationsGoldman, Nathan0Ozawa, Tomoki1CENOLI, Université Libre de Bruxelles, CP 231, Campus Plaine, B-1050 Brussels, Belgium; Laboratoire Kastler Brossel, Collège de France, CNRS, ENS-Université PSL, Sorbonne Université, 11 Place Marcelin Berthelot, 75005 Paris, FranceAdvanced Institute for Materials Research (WPI-AIMR), Tohoku University, Sendai 980-8577, JapanThis work provides a surprisingly simple demonstration that the quantized Hall conductivity of correlated insulators is given by the many-body Chern number, a topological invariant defined in the space of twisted boundary conditions. In contrast to conventional proofs, generally based on the Kubo formula, our approach entirely relies on combining Kramers–Kronig relations and Fermi’s golden rule within a circular-dichroism framework. This pedagogical derivation illustrates how the Hall conductivity of correlated insulators can be determined by monitoring single-particle excitations upon a circular drive, a conceptually simple picture with direct implications for quantum-engineered systems, where excitation rates can be directly monitored.https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.191/quantum Hall effecttopological quantum matterquantum gasesKramers–Kronig relationsquantized responsescircular dichroismmany-body Chern numbercorrelated topological insulators |
| spellingShingle | Goldman, Nathan Ozawa, Tomoki Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations Comptes Rendus. Physique quantum Hall effect topological quantum matter quantum gases Kramers–Kronig relations quantized responses circular dichroism many-body Chern number correlated topological insulators |
| title | Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations |
| title_full | Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations |
| title_fullStr | Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations |
| title_full_unstemmed | Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations |
| title_short | Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations |
| title_sort | relating the hall conductivity to the many body chern number using fermi s golden rule and kramers kronig relations |
| topic | quantum Hall effect topological quantum matter quantum gases Kramers–Kronig relations quantized responses circular dichroism many-body Chern number correlated topological insulators |
| url | https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.191/ |
| work_keys_str_mv | AT goldmannathan relatingthehallconductivitytothemanybodychernnumberusingfermisgoldenruleandkramerskronigrelations AT ozawatomoki relatingthehallconductivitytothemanybodychernnumberusingfermisgoldenruleandkramerskronigrelations |