Quench Induced Growth of Distant Entanglement from Product and Locally Entangled States in Spin Chains

We study the problem of entangling two spins at the distant ends of a spin chain by exploiting the nonequilibrium dynamics of the system after a sudden global quench. As initial states we consider a canted/spiral order product state of the spins, and singlets of neighboring pairs of spins. We find that within the class of canted order initial states, no entanglement is generated at any time except for the special case of the Neel state. While an earlier work had shown that the Neel state is indeed an excellent starting resource for the dynamical generation of long distance entanglement, the curious fact that this is the sole point within a large class of initial product states of the spins was not noted. On the other hand, we find that an initial state which is a series of nearest neighbor Bell states, and well motivated by some physical realizations, is also a good starting resource for end to end entanglement in a similar way to the Neel state.