  We study quantum quenches in the XXZ spin-$1/2$ Heisenberg chain from
families of ferromagnetic and antiferromagnetic initial states. Using Bethe
ansatz techniques, we compute short-range correlators in the complete
generalized Gibbs ensemble (GGE), which takes into account all local and
quasi-local conservation laws. We compare our results to exact diagonalization
and numerical linked cluster expansion calculations for the diagonal ensemble
finding excellent agreement and thus providing a very accurate test for the
validity of the complete GGE. Furthermore, we compute the diagonal entropy in
the post-quench steady state. By careful finite-size scaling analyses of the
exact diagonalization results, we show that the diagonal entropy is equal to
one half the Yang-Yang entropy corresponding to the complete GGE. Finally, the
complete GGE is quantitatively contrasted with the GGE built using only the
local conserved charges (local GGE). The predictions of the two ensembles are
found to differ significantly in the case of ferromagnetic initial states. Such
initial states are better suited than others considered in the literature to
experimentally test the validity of the complete GGE and contrast it to the
failure of the local GGE.
