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The generalized Gibbs ensemble has been shown to be relevant in therelaxation of a completely integrable system subject to a quantum quench, inthe sense that it accurately predicts the steady values of some physicalvariables. We proceed to further question its relevance by giving the quenchedsystem a second quench. The concern is whether the generalized Gibbs ensemblecan also accurately predict the relaxed system's response to the second quench.Two case studies with the transverse Ising model and the hard-core bosons inone dimension yield an affirmative answer. The relevance of the generalizedGibbs ensemble in the non-equilibrium dynamics of integrable systems is thengreatly strengthened.

The generalized Gibbs ensemble as a pseudo-initial state: its predictive power revealed in a second quench