  Recent experimental achievements in controlling ultracold gases in optical
lattices open a new perspective on quantum many-body physics. In these
experimental setups it is possible to study coherent time evolution of isolated
quantum systems. These dynamics reveal new physics beyond the low-energy
properties usually relevant in solid-state many-body systems. In this paper we
study the time evolution of antiferromagnetic order in the Heisenberg chain
after a sudden change of the anisotropy parameter, using various numerical and
analytical methods. As a generic result we find that the order parameter, which
can show oscillatory or non-oscillatory dynamics, decays exponentially except
for the effectively non-interacting case of the XX limit. For weakly ordered
initial states we also find evidence for an algebraic correction to the
exponential law. The study is based on numerical simulations using a numerical
matrix product method for infinite system sizes (iMPS), for which we provide a
detailed description and an error analysis. Additionally, we investigate in
detail the exactly solvable XX limit. These results are compared to
approximative analytical approaches including an effective description by the
XZ-model as well as by mean-field, Luttinger-liquid and sine-Gordon theories.
This reveals which aspects of non-equilibrium dynamics can as in equilibrium be
described by low-energy theories and which are the novel phenomena specific to
quantum quench dynamics. The relevance of the energetically high part of the
spectrum is illustrated by means of a full numerical diagonalization of the
Hamiltonian.
