In my talk I will discuss a weak ergodicity breaking relevant for the experimentally realized Rydberg-atom quantum simulator . I will concentrate on the variational description of unusual quantum many-body revivals that originate from the small set of special non-thermal eigenstates. I will relate this dynamics to presence of stable periodic trajectories within time-dependent variational principle (TDVP) description of dynamics . I will use TDVP to find new "scars" and explore their response to perturbations of the Hamiltonian in one and two spatial dimensions. For two dimensional systems I will introduce the synchronization mechanism that helps stabilizing quantum revivals and mitigates boundary effects . Finally, I will discuss a new opportunities for the creation of novel states with long-lived coherence in systems that are now experimentally realizable .
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 A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, M. Serbyn, Phys. Rev. X 10, 011055 (2020)
 A. A. Michailidis, C. J. Turner, Z. Papić, D. A. Abanin, M. Serbyn, arXiv:2003.02825