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.
|Titolo:||Validity of the GGE for quantum quenches from interacting to noninteracting models|
|Autori:||Sotiriadis S.; Calabrese P.|
|Rivista:||JOURNAL OF STATISTICAL MECHANICS: THEORY AND EXPERIMENT|
|Data di pubblicazione:||2014|
|Digital Object Identifier (DOI):||10.1088/1742-5468/2014/07/P07024|
|Appare nelle tipologie:||1.1 Journal article|