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We explore the role of the initial state on the onset of thermalization inisolated quantum many-body systems after a quench. The initial state is aneigenstate of an initial Hamiltonian $\hat{H}_I$ and it evolves according to adifferent final Hamiltonian $\hat{H}_F$. If the initial state has a chaoticstructure with respect to $\hat{H}_F$, i.e., if it fills the energy shellergodically, thermalization is certain to occur. This happens when $\hat{H}_I$is a full random matrix, because its states projected onto $\hat{H}_F$ arefully delocalized. The results for the observables then agree with thoseobtained with thermal states at infinite temperature. However, finite realsystems with few-body interactions, as the ones considered here, are deprivedof fully extended eigenstates, even when described by a nonintegrableHamiltonian. We examine how the initial state delocalizes as it gets closer tothe middle of the spectrum of $\hat{H}_F$, causing the observables to approachthermal averages, be the models integrable or chaotic. Our numerical studiesare based on initial states with energies that cover the entire lower half ofthe spectrum of one-dimensional Heisenberg spin-1/2 systems.

Effects of the interplay between initial state and Hamiltonian on the thermalization of isolated quantum many-body systems