Localizable entanglement in antiferromagnetic spin chains

Abstract

Antiferromagnetic spin chains play an important role in condensed matter and statistical mechanics. Recently $\mathit{XXX}$ spin chain was discussed in relation to information theory. Here we consider localizable entanglement. It is how much entanglement can be localized on two spins by performing local measurements on other individual spins (in a system of many interacting spins). We consider the ground state of antiferromagnetic spin chain. We study localizable entanglement [represented by concurrence] between two spins. It is a function of the distance. We start with isotropic spin chain. Then we study effects of anisotropy and magnetic field. We conclude that anisotropy increases the localizable entanglement. We discovered high sensitivity to a magnetic field in cases of high symmetry. We also evaluated concurrence of these two spins before the measurement to illustrate that the measurement raises the concurrence.