  We study quenches in integrable spin-1/2 chains in which we evolve the ground
state of the antiferromagnetic Ising model with the anisotropic Heisenberg
Hamiltonian. For this nontrivially interacting situation, an application of the
first-principles-based quench action method allows us to give an exact
description of the postquench steady state in the thermodynamic limit. We show
that a generalized Gibbs ensemble, implemented using all known local conserved
charges, fails to reproduce the exact quench action steady state and to
correctly predict postquench equilibrium expectation values of physical
observables. This is supported by numerical linked-cluster calculations within
the diagonal ensemble in the thermodynamic limit.
