  We study stationary states emerging after global quenches in which the time
evolution is under local Hamiltonians that possess semilocal conserved
operators. In particular, we study a model that is dual to quantum XY chain. We
show that a localized perturbation in the initial state can turn an exponential
decay of spatial correlations in the stationary state into an algebraic decay.
We investigate the consequences on the behavior of the (R\'enyi-$\alpha$)
entanglement entropies, focusing on the tripartite information of three
adjacent subsystems. In the limit of large subsystems, we show that in the
stationary state with the algebraic decay of correlations the tripartite
information exhibits a non-zero value with a universal dependency on the cross
ratio, while it vanishes in the stationary state with the exponential decay of
correlations.
