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Following our previous work [PRL 113 (2014) 09020] we present here a detailedcomparison of the quench action approach and the predictions of the generalizedGibbs ensemble, with the result that while the quench action formalismcorrectly captures the steady state, the GGE does not give a correctdescription of local short-distance correlation functions. We extend ourstudies to include another initial state, the so-called q-dimer state. Wepresent important details of our construction, including new results concerningexact overlaps for the dimer and q-dimer states, and we also give an exactsolution of the quench-action-based overlap-TBA for the q-dimer. Furthermore,we extend our computations to include the xx spin correlations besides the zzcorrelations treated previously, and give a detailed discussion of theunderlying reasons for the failure of the GGE, especially in the light of newdevelopments.

Quenching the XXZ spin chain: quench action approach versus generalized Gibbs ensemble