  We study the time evolution of the entanglement entropy in the short and
long-range coupled harmonic oscillators that have well-defined continuum limit
field theories. We first introduce a method to calculate the entanglement
evolution in generic coupled harmonic oscillators after quantum quench. Then we
study the entanglement evolution after quantum quench in harmonic systems that
the couplings decay effectively as $1/r^{d+\alpha}$ with the distance $r$.
After quenching the mass from non-zero value to zero we calculate numerically
the time evolution of von Neumann and R\'enyi entropies. We show that for
$1<\alpha<2$ we have a linear growth of entanglement and then saturation
independent of the initial state. For $0<\alpha<1$ depending on the initial
state we can have logarithmic growth or just fluctuation of entanglement. We
also calculate the mutual information dynamics of two separated individual
harmonic oscillators. Our findings suggest that in our system there is no
particular connection between having a linear growth of entanglement after
quantum quench and having a maximum group velocity or generalized Lieb-Robinson
bound.
