Using time-dependent density matrix renormalization group (tDMRG), we analyze the time evolution of density-density correlations in one-dimensional spinless fermion systems after a global quench of the Hamiltonian. In particular, quenches to free fermion systems are considered. In this case, the time evolution can in fact be obtained exactly up to arbitrary times when providing the four-point propagators of the initial state, which are computed via DMRG at high accuracy. Taking this approach, we are able to both study the dynamics directly after the quench, as well as the long-time behavior. We obtain a ballistic lightcone structure and study the region outside in detail. For gapless initial states, we observe temporal oscillation outside the lightcone which we relate to the initial state and the dispersion relation of the quenched Hamiltonian.
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