Supplementary Material for EPAPS Quenching the Anisotropic Heisenberg Chain: Exact Solution and Generalized Gibbs Ensemble

By assumption the extensive part of the overlap coefficient S[ρ] is smooth and does not depend on finite size differences within the set of Bethe states that scale to the same densities ρ. The number of Bethe states for each set of distributions ρ is given by the extensive Yang-Yang entropy [1]: eY Y . We are then free to select a representative finite size Bethe state out of all states that scale to the same ρ. We consider the state |{λj}j=1〉 consisting of 2ns strings such that 2ns = ∑∞ n=1Mn, where Mn is the number of n-strings in the state and we choose all Mn to be even. Note that this is one possible choice for a representative state. Different choices regarding the eveness of the fillings {Mn}n=1 lead to different expressions for the exact overlap formula (S4), but are believed [2, 3] to have the same extensive smooth part S[ρ]. For any finite size N , Bethe states are organized in deviated strings. We use the following notation to label the rapidities of such states: