  In this work we study the time evolution of Renyi entanglement entropy for
locally excited states created by twist operators in cyclic orbifold
$(T^2)^n/\mathbb{Z}_n$ and symmetric orbifold $(T^2)^n/S_n$. We find that when
the square of its compactification radius is rational, the second Renyi entropy
approaches a universal constant equal to the logarithm of the quantum dimension
of the twist operator. On the other hand, in the non-rational case, we find a
new scaling law for the Renyi entropies given by the double logarithm of time
$\log\log t$ for the cyclic orbifold CFT.
