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

In the majority of analytical verifications of the conjecture that the Generalized Gibbs Ensemble (GGE) describes the large time asymptotics of local observables in quantum quench problems, both post- and pre-quench Hamiltonians are essentially noninteracting. We test this conjecture studying 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 this conjecture is more generally valid for 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.