  It has been recently observed for a particular quantum quench in the XXZ spin
chain that local observables do not equilibrate to the predictions of the
Generalized Gibbs Ensemble (GGE). In this work we argue that the breakdown of
the GGE can be attributed to the failure of the Generalized Eigenstate
Thermalization Hypothesis (GETH), which has been the main candidate to explain
the validity of the GGE. We provide explicit counterexamples to the GETH and
argue that generally it does not hold in models with multiple particle species.
Therefore there is no reason to assume that the GGE should describe the long
time limit of observables in these integrable models.
