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In weakly perturbed systems that are close to integrability, thermalizationcan be delayed by the formation of prethermalization plateaus. We study thebuild-up of density-density correlations after a weak interaction quench in theHubbard model in $d > 1$ dimensions using unitary perturbation theory. Startingfrom a pre-quench state at temperature $T$, we show that the prethermalizationvalues of the post-quench correlations are equal to the equilibrium values ofthe interacting model at the same temperature $T$. This is explained by thelocal character of density-density correlations.

Prethermalization of density-density correlations after an interaction quench in the Hubbard model