  We consider an infinite one dimensional anisotropic XY spin chain with a
nearest neighbor time-dependent Heisenberg coupling J(t) between the spins in
presence of a time-dependent magnetic field h(t). We discuss a general solution
for the system and present an exact solution for particular choice of J and h
of practical interest. We investigate the dynamics of entanglement for
different degrees of anisotropy of the system and at both zero and finite
temperatures. We find that the time evolution of entanglement in the system
show non-ergodic and critical behavior at zero and finite temperatures and
different degrees of anisotropy. The asymptotic behavior of entanglement at the
infinite time limit at zero temperature and constant J and h depends only the
parameter lambda=J/h rather than the individual values of J and h for all
degrees of anisotropy but changes for nonzero temperature. Furthermore, the
asymptotic behavior is very sensitive to the initial values of J and h and for
particular choices we may create finite asymptotic entanglement regardless of
the final values of J and h. The persistence of quantum effects in the system
as it evolves and as the temperature is raised is studied by monitoring the
entanglement. We find that the quantum effects dominates within certain regions
of the kT-lambda space that vary significantly depending on the degree of the
anisotropy of the system. Particularly, the quantum effects in the Ising model
case persists in the vicinity of both its critical phase transition point and
zero temperature as it evolves in time. Moreover, the interplay between the
different system parameters to tune and control the entanglement evolution is
explored.
