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We study the dynamics and thermalization of strongly correlated fermions infinite one-dimensional lattices after a quantum quench. Our calculations areperformed using exact diagonalization. We focus on one- and two-bodyobservables such as the momentum distribution function [n(k)] and thedensity-density structure factor [N(k)], respectively, and study the effects ofapproaching an integrable point. We show that while the relaxation dynamics andthermalization of N(k) for fermions is very similar to the one of hardcorebosons, the behavior of n(k) is distinctively different. The latter observableexhibits a slower relaxation dynamics in fermionic systems. We identify theorigin of this behavior, which is related to the off-diagonal matrix elementsof n(k) in the basis of the eigenstates of the Hamiltonian. More generally, wefind that thermalization occurs far away from integrability and that it breaksdown as one approaches the integrable point.

Quantum quenches and thermalization in one-dimensional fermionic systems