Relaxation of antiferromagnetic order in spin-1/2 chains following a   quantum quench
  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. 
Peter Barmettler, Matthias Punk, Vladimir Gritsev, Eugene Demler, Ehud   Altman