One-Half Topological Number in Entangled Quantum Physics

• URL: http://arxiv.org/abs/2308.14062v3
• Date: Tue, 27 Feb 2024 07:49:16 GMT
• Title: One-Half Topological Number in Entangled Quantum Physics
• Authors: Karyn Le Hur
• Abstract summary: A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing a hedgehog structure as a result of a radial magnetic field. We show applications of entangled wavefunctions in band structures, introducing a local topological marker in momentum space.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: A topological phase can be engineered in quantum physics from the Bloch sphere of a spin-1/2 showing an hedgehog structure as a result of a radial magnetic field. We elaborate on a relation between the formation of an entangled wavefunction at one pole, in a two-spins model, and an interesting pair of one-half topological numbers. Similar to Cooper pairs in superconductors, the Einstein-Podolsky-Rosen pair or Bell state produces a half flux quantization, which here refers to the halved flux of the Berry curvature on the surface. These 1/2-numbers also reveal the presence of a free Majorana fermion at a pole. The topological responses can be measured when driving from north to south and also from a circularly polarized field at the poles revealing the quantized or half-quantized nature of the protected transverse currents. We show applications of entangled wavefunctions in band structures, introducing a local topological marker in momentum space, to characterize the topological response of two-dimensional semimetals in bilayer geometries.

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