[Une démonstration du lien entre la conductivité de Hall et le nombre de Chern pour le problème à N corps, basée sur la règle d’or de Fermi et les relations de Kramers-Kronig]
Ce travail présente une démonstration simple et originale du lien qui relie la conductivité de Hall quantifiée des isolants corrélés au nombre de Chern du problème à N corps, un invariant topologique défini dans l’espace des conditions aux bords généralisées. Contrairement aux démonstrations conventionnelles, qui sont généralement basées sur la formule de Kubo, cette approche s’appuie entièrement sur les relations de Kramers-Kronig et la règle d’or de Fermi, dans le cadre du dichroisme circulaire. Cette dérivation pédagogique illustre un fait remarquable, à savoir que la conductivité de Hall des isolants corrélés peut être déterminée en mesurant des excitations à un corps sous l’effet d’une force circulaire. Cette observation est particulièrement pertinente pour les systèmes quantiques topologiques pour lesquels les taux d’excitation peuvent être directement mesurés au laboratoire.
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.
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Mot clés : effets Hall quantiques, états topologiques de la matière, matière quantique fortement corrélée, dichroisme circulaire, règle d’or de Fermi, relations de Kramers-Kronig
Nathan Goldman 1, 2 ; Tomoki Ozawa 3
CC-BY 4.0
@article{CRPHYS_2024__25_G1_289_0,
author = {Nathan Goldman and Tomoki Ozawa},
title = {Relating the {Hall} conductivity to the many-body {Chern} number using {Fermi{\textquoteright}s} {Golden} rule and {Kramers{\textendash}Kronig} relations},
journal = {Comptes Rendus. Physique},
pages = {289--302},
publisher = {Acad\'emie des sciences, Paris},
volume = {25},
year = {2024},
doi = {10.5802/crphys.191},
language = {en},
}
TY - JOUR AU - Nathan Goldman AU - Tomoki Ozawa TI - Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations JO - Comptes Rendus. Physique PY - 2024 SP - 289 EP - 302 VL - 25 PB - Académie des sciences, Paris DO - 10.5802/crphys.191 LA - en ID - CRPHYS_2024__25_G1_289_0 ER -
%0 Journal Article %A Nathan Goldman %A Tomoki Ozawa %T Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations %J Comptes Rendus. Physique %D 2024 %P 289-302 %V 25 %I Académie des sciences, Paris %R 10.5802/crphys.191 %G en %F CRPHYS_2024__25_G1_289_0
Nathan Goldman; Tomoki Ozawa. Relating the Hall conductivity to the many-body Chern number using Fermi’s Golden rule and Kramers–Kronig relations. Comptes Rendus. Physique, Volume 25 (2024), pp. 289-302. doi : 10.5802/crphys.191. https://comptes-rendus.academie-sciences.fr/physique/articles/10.5802/crphys.191/
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