Thermalization in systems with bipartite eigenmode entanglement

It is analytically shown that the asymptotic correlations following a quantum quench in exactly solvable models can sometimes look essentially thermal provided the initial coupling between the system eigenmodes induces a large gap. We study this phenomenon using simple models, which also illustrate the relationship between the entanglement spectrum of the initial state and the generalized Gibbs ensemble describing the long-time correlations after the quench. We also show that the effective temperature characterizing the correlations is not related to the energy fluctuations after the quench, and therefore does not have thermodynamic meaning. The latter observation implies a breakdown of the fluctuation-dissipation theorem. (paper)