Entanglement evolution of a spin chain bath in driving the decoherence of a coupled quantum spin

For an electron spin in coupling with an interacting spin chain via hyperfine-type interaction, we investigate the dynamical evolutions of the pairwise entanglement of the spin chain and a correlation function joined the electron spin with a pair of chain spins in correspondence to the electron spin coherence evolution. Both quantities manifest a periodic and a decaying evolution. The entanglement of the spin bath is significant in distinguishing the zero-coherence status exhibited in periodic and decoherence evolutions of the electron spin. The periodical concurrence evolution of the spin bath characterizes the whole system in a coherence-preserving phase, particularly for the case that the associated periodic coherence evolution is predominated by zero-value in the infinite chain-length limit, which was often regarded as the realization of decoherence.