  Motivated by recent experiments with ultra-cold quantum gases in optical
lattices we study the decay of the staggered moment in the one-dimensional
Fermi-Hubbard model starting from a perfect Neel state using exact
diagonalization and the iTEBD method. This extends previous work in which the
same problem has been addressed for pure spin Hamiltonians. As a main result,
we show that the relaxation dynamics of the double occupancy and of the
staggered moment are different. The former is controlled by the
nearest-neighbor tunneling rate while the latter is much slower and strongly
dependent on the interaction strength, indicating that spin excitations are
important. This difference in characteristic energy scales for the fast charge
dynamics and the much slower spin dynamics is also reflected in the real-time
evolution of nearest-neighbor density and spin correlations. A very interesting
time dependence emerges in the von Neumann entropy, which at short times
increases linearly with a slope proportional to the tunneling matrix element
while the long-time growth of entanglement is controlled by spin excitations.
Our predictions for the different relaxation dynamics of the staggered moment
and the double occupancy should be observable in state-of-the art optical
lattice experiments. We further compare time averages of the double occupancy
to both the expectation values in the canonical and diagonal ensemble, which
quantitatively disagree with each other on finite systems. We relate the
question of thermalization to the eigenstate thermalization hypothesis.
