Validity of the GGE for quantum quenches from interacting to noninteracting models

TL;DR

This work analyzes quantum quenches where the post-quench Hamiltonian is noninteracting but the pre-quench Hamiltonian can be interacting, testing the Generalised Gibbs Ensemble (GGE) description beyond Gaussian initial states.The authors show that the stationary, local multi-point correlations are determined by the cluster decomposition property of the initial state: if the initial state satisfies cluster decomposition, the stationary values agree with the GGE; if not, memory of initial correlations persists and the GGE fails.They derive explicit results for relativistic and nonrelativistic bosonic theories, demonstrating that the two-point function always matches the GGE under broad conditions, while the four-point function tests reveal the crucial role of initial-state correlations beyond two-point functions; for the Lieb–Liniger quench to zero interaction, the g1 result is tautological and g2 shows a power-law relaxation controlled by the Luttinger parameter $K$ before settling into the GGE prediction.Overall, the paper identifies cluster decomposition as the fundamental criterion governing GGE validity in quenches from interacting to noninteracting models and provides analytical connections to earlier numerical findings in integrable systems.

Abstract

In the majority of the analytical verifications of the conjecture that the Generalised Gibbs Ensemble describes the large time asymptotics of local observables in quantum quench problems, both the post-quench and the pre-quench Hamiltonians are essentially noninteracting. We test this conjecture studying the field correlations in the more general case of an arbitrary pre-quench Hamiltonian, while keeping the post-quench one noninteracting. We first show that in the previously studied special case of a noninteracting pre-quench Hamiltonian, the validity of the conjecture is a consequence of Wick's theorem. We then show that it is also valid in the general case of an arbitrary interacting pre-quench Hamiltonian, but this time as a consequence of the cluster decomposition property of the initial state, which is a fundamental principle for generic physical states. For arbitrary initial states that do not satisfy the cluster decomposition property, the above conjecture is not generally true. As a byproduct of our investigation we obtain an analytical derivation of earlier numerical results for the large time evolution of correlations after a quantum quench of the interaction in the Lieb-Liniger model from a nonzero value to zero.