Entanglement of spin- $$\varvec{1/2}$$ 1 / 2 Heisenberg antiferromagnetic quantum spin chains

Abstract

The quantum entanglement measure is determined, for the first time, for a collection of spin-1 / 2 arranged in a infinite chain with finite temperature and applied to a single-crystal \(\beta \)-\({\hbox {T}_{\mathrm{e}}\hbox {VO}_4}\). The physical quantity proposed here to measure the entanglement is the distance between states by adopting the Hilbert–Schmidt norm. We relate the distance between states with the magnetic susceptibility. The decoherence temperature, above which the entanglement is suppressed, is determined for a system. A correlation among their decoherence temperatures and their respective exchange coupling constants is established; moreover, it is conjectured that the exchange coupling protects the system from decoherence as temperature increases.