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It has been recently observed for a particular quantum quench in the XXZ spinchain that local observables do not equilibrate to the predictions of theGeneralized Gibbs Ensemble (GGE). In this work we argue that the breakdown ofthe GGE can be attributed to the failure of the Generalized EigenstateThermalization Hypothesis (GETH), which has been the main candidate to explainthe validity of the GGE. We provide explicit counterexamples to the GETH andargue 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 longtime limit of observables in these integrable models.

Failure of the Generalized Eigenstate Thermalization Hypothesis in integrable models with multiple particle species