Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866909305441091584 |
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| author | Goldman, Nathan Ozawa, Tomoki |
| author_facet | Goldman, Nathan Ozawa, Tomoki |
| contents | This pedagogical piece 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 | Preprint |
| id |
arxiv_https___arxiv_org_abs_2403_03340 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations Goldman, Nathan Ozawa, Tomoki Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Quantum Physics This pedagogical piece 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. |
| title | Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations |
| topic | Mesoscale and Nanoscale Physics Quantum Gases Strongly Correlated Electrons Quantum Physics |
| url | https://arxiv.org/abs/2403.03340 |