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

TL;DR

This paper demonstrates that the Generalized Eigenstate Thermalization Hypothesis (GETH) fails in integrable models with multiple particle species, explaining why the Generalized Gibbs Ensemble (GGE) does not always predict long-term observable behavior.

Contribution

The work provides explicit counterexamples to GETH, showing its failure in models with multiple particle species, challenging assumptions about GGE's applicability.

Findings

GETH does not hold in models with multiple particle species

GGE predictions fail for certain integrable models

Counterexamples demonstrate GETH's limitations

Abstract

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.