  We study the real time evolution of the correlation functions in a globally
quenched interacting one dimensional lattice system by means of time adaptive
density matrix renormalization group. We find a clear light-cone behavior
quenching the repulsive interaction from the gapped density wave regime. The
spreading velocity increases with the final values of the interaction and then
saturates at a certain finite value. In the case of a Luttinger liquid phase as
the initial state, for strong repulsive interaction quenches, a more complex
dynamics occurs as a result of bound state formations. From the other side in
the attractive regime, depending on where connected correlation functions are
measured, one can observe a delay in the starting time evolution and a
coexistence of ballistic and localized signals.
