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

Autor:	Goldman, Nathan, Ozawa, Tomoki
Rok vydání:	2024
Předmět:	Condensed Matter - Mesoscale and Nanoscale Physics Condensed Matter - Quantum Gases Condensed Matter - Strongly Correlated Electrons Quantum Physics
Zdroj:	Comptes Rendus Physique 25, 289 (2024)
Druh dokumentu:	Working Paper
DOI:	10.5802/crphys.191
Popis:	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. Comment: 8 pages, 2 figures + Appendix
Databáze:	arXiv
Externí odkaz:	http://arxiv.org/abs/2403.03340 Zobrazit plný text záznamu View this record from Arxiv