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Comptes Rendus Physique
Article . 2024 . Peer-reviewed
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Article . 2024
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https://dx.doi.org/10.48550/ar...
Article . 2024
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Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations

Authors: Goldman, Nathan; Ozawa, Tomoki;

Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations

Abstract

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.

Country
France
Keywords

Quantum Physics, Condensed Matter - Mesoscale and Nanoscale Physics, Strongly Correlated Electrons (cond-mat.str-el), Physics, QC1-999, FOS: Physical sciences, quantum Hall effect, circular dichroism, Condensed Matter - Strongly Correlated Electrons, Quantum Gases (cond-mat.quant-gas), Mesoscale and Nanoscale Physics (cond-mat.mes-hall), topological quantum matter, many-body Chern number, correlated topological insulators, quantized responses, quantum gases, Condensed Matter - Quantum Gases, Quantum Physics (quant-ph), [PHYS.COND] Physics [physics]/Condensed Matter [cond-mat], [PHYS.QPHY] Physics [physics]/Quantum Physics [quant-ph], Kramers–Kronig relations

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    influence
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selected citations
These citations are derived from selected sources.
This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Citations provided by BIP!
popularity
This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.
BIP!Popularity provided by BIP!
influence
This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).
BIP!Influence provided by BIP!
impulse
This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.
BIP!Impulse provided by BIP!
3
Top 10%
Average
Average
Green
gold