  Following our previous work [PRL 113 (2014) 09020] we present here a detailed
comparison of the quench action approach and the predictions of the generalized
Gibbs ensemble, with the result that while the quench action formalism
correctly captures the steady state, the GGE does not give a correct
description of local short-distance correlation functions. We extend our
studies to include another initial state, the so-called q-dimer state. We
present important details of our construction, including new results concerning
exact overlaps for the dimer and q-dimer states, and we also give an exact
solution of the quench-action-based overlap-TBA for the q-dimer. Furthermore,
we extend our computations to include the xx spin correlations besides the zz
correlations treated previously, and give a detailed discussion of the
underlying reasons for the failure of the GGE, especially in the light of new
developments.
