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In thermal equilibrium, the fluctuation-dissipation theorem relates thelinear response and correlation functions in a model and observable independentfashion. Out of equilibrium, these relations still hold if the equilibriumtemperature is replaced by an observable and frequency-dependent parameter(effective temperature). When the system achieves a long time thermal state allof these effective temperatures should be equal and constant. Following thisapproach we examine the long times regime after a quantum quench in a systemwith bipartite entanglement in which the asymptotic values of the observableare compatible with the ones obtained in a Gibbs ensemble. We observe that whenthe initial entanglement is large, and for a large range of (intermediate)frequencies, the effective temperatures corresponding to the analyzed local andnon-local operators approach an approximate constant value equal to thetemperature that governs the decay of correlations. Still, the residualfrequency dependence in the effective temperature, and the differences observedamong observables discards strict thermalization.

Effective temperature from fluctuation-dissipation theorem in systems with bipartite eigenmode entanglement