Failure of the local generalized Gibbs ensemble for integrable models with bound states

In this work we study the applicability of the local generalized Gibbs ensemble (GGE) to integrable one-dimensional systems with bound states. We find that the GGE, when defined using only local conserved quantities, fails to describe the long-time dynamics for most initial states, including eigenstates. We present our calculations by studying the attractive Lieb-Liniger gas and the $XXZ$ magnet, although similar results may be obtained for other models.