One-Half Topological Number in Entangled Quantum Physics

TL;DR

This paper explores a novel half-integer topological number in entangled quantum systems, linking it to Majorana fermions and quantized responses, with applications in topological band structures and semimetals.

Contribution

It introduces a new half-integer topological number associated with entangled wavefunctions and demonstrates its implications for topological responses and Majorana fermions.

Findings

Half flux quantization linked to entangled pairs.

Presence of free Majorana fermions at poles.

Quantized transverse currents in topological responses.

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.