  We study the unitary time evolution of antiferromagnetic order in anisotropic
Heisenberg chains that are initially prepared in a pure quantum state far from
equilibrium. Our analysis indicates that the antiferromagnetic order imprinted
in the initial state vanishes exponentially. Depending on the anisotropy
parameter, oscillatory or non-oscillatory relaxation dynamics is observed.
Furthermore, the corresponding relaxation time exhibits a at the critical
point, in contrast to the usual notion of critical slowing down, from which a
maximum is expected.
