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Exact steady states for quantum quenches in integrable Heisenberg spin chains

The study of quantum quenches in integrable systems has significantly advanced with the introduction of the Quench Action method, a versatile analytical approach to non-equilibrium dynamics. However, its application is limited to those cases where the overlaps between the initial state and the eigenstates of the Hamiltonian governing the time evolution are known exactly. Conversely, in this work we consider physically interesting initial states for which such overlaps are still unknown. In particular, we focus on different classes of product states in spin-$1/2$ and spin-$1$ integrable chains, such as tilted ferromagnets and antiferromagnets. We get around the missing overlaps by following a recent approach based on the knowledge of complete sets of quasi-local charges. This allows us to provide a closed-form analytical characterization of the effective stationary state reached at long times after the quench, through the Bethe ansatz distributions of particles and holes. We compute the asymptotic value of local correlations and check our predictions against numerical data.