Relating the Hall conductivity to the many-body Chern number using Fermi's Golden rule and Kramers-Kronig relations
arXiv:2403.03340 · doi:10.5802/crphys.191
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.
arXiv comment8 pages, 2 figures + Appendix
References in corpus (33)
- Quantum Spin Hall Effect in Graphene
- Quantum Spin Hall Effect and Topological Phase Transition in HgTe Quantum Wells
- Topological Order and the Quantum Spin Hall Effect
- Quantum Spin Hall Insulator State in HgTe Quantum Wells
- Berry Phase Effects on Electronic Properties
- Topological Photonics
- Quantum Spin Hall Effect
- Topological Bands for Ultracold Atoms
- Single particle Green's functions and interacting topological insulators
- Polarization and localization in insulators: generating function approach
- Bulk-boundary correspondence of topological insulators from their Green's functions
- Simplified topological invariants for interacting insulators
- Topological Order Parameters for Interacting Topological Insulators
- Measuring quantized circular dichroism in ultracold topological matter
- Experimental Measurement of the Quantum Metric Tensor and Related Topological Phase Transition with a Superconducting Qubit
- Dichroic f-sum rule and the orbital magnetization of crystals
- Realization of a fractional quantum Hall state with ultracold atoms
- Probing topology by "heating": Quantized circular dichroism in ultracold atoms
- Local Berry curvature signatures in dichroic angle-resolved photoelectron spectroscopy
- Experimental measurement of the quantum geometric tensor using coupled qubits in diamond
- A Characterization of Topological Insulators: Chern Numbers for a Ground State Multiplet
- How Circular Dichroism in time- and angle-resolved photoemission can be used to spectroscopically detect transient topological states in graphene
- Detecting fractional Chern insulators through circular dichroism
- Many-body Chern number without integration
- Quantization in chiral higher order topological insulators: circular dichroism and local Chern marker
- Fractional Chern insulators of few bosons in a box: Hall plateaus from center-of-mass drifts and density profiles
- Probing localization and quantum geometry by spectroscopy
- Connecting the Many-Body Chern Number to Luttinger's Theorem through Středa's Formula
- Tracing the nonequilibrium topological state of Chern insulators
- Quantized Rabi Oscillations and Circular Dichroism in Quantum Hall Systems
- Interacting Stochastic Topology and Mott Transition from Light Response
- Global and Local Topological Quantized Responses from Geometry, Light and Time
- Detecting chiral pairing and topological superfluidity using circular dichroism
Cited by in corpus (4)
- Theory of Generalized Landau Levels and Implication for non-Abelian States
- Circular Dichroism on the Edge of Quantum Hall Systems: From Many-Body Chern Number to Anisotropy Measurements
- Quantized and nonquantized Hall response in topological Hatsugai-Kohmoto systems
- Pressure-Tunable Generalized Wigner Crystal and Fractional Chern Insulator in twisted MoTe