Spin Entanglement of Two delocalised Fermions and Berry Phase

Abstract

We have studied the entanglement of identical fermions in two spatial regions in terms of the Berry phase acquired by their spins. The analysis is done from the viewpoint of the geometrical interpretation of entanglement, where a fermion is visualized as a scalar particle attached with a magnetic flux quantum. The quantification of spin entanglement in terms of their Berry phases is novel and generalises the relationship between the entanglement of distinguishable spins and that of delocalised fermions.