Failure of the GGE hypothesis for integrable models with bound states

TL;DR

This work examines whether the generalized Gibbs ensemble (GGE) can capture the late-time states of integrable 1D systems that support bound states. The authors show that for the attractive Lieb–Liniger gas and the XXZ model, fixed values of local conserved charges $\{I_i\}$ do not uniquely determine the post-quench state, because there exist infinitely many string-density configurations with the same $I_i^0$, and the GGE selects only one pure-state representative by maximizing the Yang–Yang entropy under the thermodynamic Bethe Ansatz constraints. Consequently, the GGE fails to describe the long-time dynamics for most initial states, including many eigenstates. This suggests that nonlocal conserved quantities or alternative ensemble formulations may be required to achieve a complete description of equilibration in bound-state integrable systems.

Abstract

In this work we study the applicability of the GGE to integrable one dimensional systems with bound states. We find that the GGE fails to describe the long time dynamics for most initial states including eigenstates. We present our calculations studying the attractive Lieb-Liniger gas and the XXZ magnet, though similar results may be obtained for other models.

Figures (1)

• Figure 1: The logic of the GGE argument. A) Attractive Lieb-Liniger model. There are many exact eigenstates whose particle densities are different but which correspond to the same conserved quantities $I_{i}^{0}$. The $I_{i}^{0}$ however determine a unique GGE density matrix which corresponds to a specific pure state. B) Repulsive Lieb-Liniger model. For each set of conserved quantities there is only one quasiparticle density which corresponds to one GGE density matrix which is then equivalent to the original quasiparticle density.