2020/08/16 by Chon-Fai Kam, Ren-Bao Liu · 4 citations
Chemistry · Physics and Astronomy · #Fullerene Chemistry and Applications #Geometric phase #MAJORANA #Phase (matter) #Quantum #Quantum Mechanics and Non-Hermitian Physics #Quantum entanglement #Quantum state #Spins #Topological Materials and Phenomena #quant-ph
paper · pdf · doi:10.1088/1367-2630/ac0ed5
published in New Journal of Physics 23(7), 073020 (IOP Publishing)
arxiv created 2020/08/16 · openalex created_date 2020/08/21 · openalex publication_date 2021/06/25 · arxiv updated 2021/08/11 · openalex updated_date 2026/08/05
Abstract Majorana stars, the antipodal directions associated with the coherent states that are orthogonal to a spin state, provide a visualization and a geometric understanding of the structures of general quantum states. For example, the Berry phase of a spin-1/2 is given by half the solid angle enclosed by the close path of its Majorana star. It is conceivable that the Berry phase of higher spins may also be related to the geometry of the Majorana constellation. We find that for a spin-1 state, besides the expected contributions from the solid angles enclosed by the close paths of the two Majorana stars, the Berry phase includes a term related to the twist of the relative position vector around the barycenter vector of the two Majorana stars, i.e., the self-rotation of the constellation. Interestingly, if the spin-1 state is taken as a symmetrized two-qubit state, the extra contribution to the Berry phase is given by the self-rotation of the Majorana constellation weighted by the quantum entanglement of the two qubits. This discovery alludes to the relevance of the Majorana stellar geometry in representing the deep structures of quantum states and of quantum entanglement.