  We study the time evolution of the two-point correlation functions in the XXZ
Heisenberg chain after a finite-time quantum quench in the anisotropy. We
compare results from numerical simulations to ones obtained in the Luttinger
model and find good agreement. We analyse the spreading of the correlations and
the associated light-cone features. We observe a delay in the appearance of the
light cone as compared to the sudden-quench setup, and link this delay to the
properties of the quench protocol.
