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We study stationary states emerging after global quenches in which the timeevolution is under local Hamiltonians that possess semilocal conservedoperators. In particular, we study a model that is dual to quantum XY chain. Weshow that a localized perturbation in the initial state can turn an exponentialdecay 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 threeadjacent subsystems. In the limit of large subsystems, we show that in thestationary state with the algebraic decay of correlations the tripartiteinformation exhibits a non-zero value with a universal dependency on the crossratio, while it vanishes in the stationary state with the exponential decay ofcorrelations.

Universality in the tripartite information after global quenches: spin flip and semilocal charges