Quantum Entangled Fractional Topology and Curvatures

• Published in: Communications Physics
• Main Authors: Hutchinson, Joel, Hur, Karyn Le
• Other Authors: Centre de Physique Théorique Palaiseau (CPHT), Centre National de la Recherche Scientifique (CNRS)-École polytechnique (X)
• Format: Article in Journal/Newspaper
• Language: English
• Published: HAL CCSD 2021
• Subjects: topology; fractional; curvature; magnetic field; Poincare; model; quantum mechanics; [PHYS.PHYS.PHYS-GEN-PH]Physics [physics]/Physics [physics]/General Physics [physics.gen-ph]; [PHYS.HTHE]Physics [physics]/High Energy Physics - Theory [hep-th]; [PHYS.MPHY]Physics [physics]/Mathematical Physics [math-ph]; [PHYS.COND]Physics [physics]/Condensed Matter [cond-mat]; [PHYS.QPHY]Physics [physics]/Quantum Physics [quant-ph]; North Pole; South Pole; South pole
• Online Access: https://hal.archives-ouvertes.fr/hal-02507659; https://doi.org/10.1038/s42005-021-00641-0

International audience We propose a two-spin quantum-mechanical model with applied magnetic fields acting on the Poincaré-Bloch sphere, to reveal a new class of topological energy bands with Chern number one half for each spin-1/2. The mechanism behind this fractional topology is a two-spin product state at the north pole and a maximally entangled state close to the south pole. The fractional Chern number of each spin can be measured through the magnetizations at the poles. We study a precise protocol where the spin dynamics in time reflects the Landau-Zener physics associated with energy band crossing effects. We show a correspondence between the two-spin system and topological bilayer models on a honeycomb lattice. These models describe semimetals with a nodal ring surrounding the region of entanglement.