Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations - Archive ouverte HAL Access content directly
Preprints, Working Papers, ... Year : 2024

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

Abstract

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.

Dates and versions

hal-04523184 , version 1 (27-03-2024)

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Nathan Goldman, Tomoki Ozawa. Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations. 2024. ⟨hal-04523184⟩
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