Quantum Entangled Fractional Topology and Curvatures

• Main Authors: Hutchinson, Joel, Hur, Karyn Le
• Format: Article in Journal/Newspaper
• Language: unknown
• Published: arXiv 2020
• Subjects: Mesoscale and Nanoscale Physics cond-mat.mes-hall; Strongly Correlated Electrons cond-mat.str-el; High Energy Physics - Theory hep-th; Mathematical Physics math-ph; Quantum Physics quant-ph; FOS Physical sciences; North Pole; South Pole; South pole
• Online Access: https://dx.doi.org/10.48550/arxiv.2002.11823; https://arxiv.org/abs/2002.11823

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. : Main text is 29 pages, 3 figures. Supplementary Information attached is 28 pages, 12 figures