Quantum Entangled Fractional Topology and Curvatures

Abstract

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

References in corpus (8)

• Topological Photonics
• Time-reversal symmetry breaking in circuit-QED based photon lattices
• Observation of Berry's Phase in a Solid State Qubit
• Observation of topological transitions in interacting quantum circuits
• Measuring a topological transition in an artificial spin 1/2 system
• Interacting Stochastic Topology and Mott Transition from Light Response
• Topology of a dissipative spin: dynamical Chern number, bath induced non-adiabaticity and a quantum dynamo effect
• Interacting topological frequency converter

Cited by in corpus (6)

• Global and Local Topological Quantized Responses from Geometry, Light and Time
• Analytical approach for the Mott transition in the Kane-Mele-Hubbard model
• Spin-orbit coupling in the kagome lattice with flux and time-reversal symmetry
• A topologically protected quantum dynamo effect in a driven spin-boson model
• A Model for Topological p-wave Superconducting Wires with Disorder and Interactions
• Quantum Hall and Light Responses in a 2D Topological Semimetal