Exact ``towers'' of quantum many-body scar states are recently discovered sets of states in some many-body nonintegrable systems. They are evenly spaced in energy and do not obey the eigenstate thermalization hypothesis. Here, the authors provide a unified framework of proving several towers of states known in the literature. This sheds light on the general structure of exact scar towers, and on the specific models themselves: the 1D AKLT models, spin-1 XY model, and a spin-{} domain wall conserving model. In particular, they provide a simple proof for the scars in the AKLT models and discover a ``pyramid'' of exact states in the spin-{} model.
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Mark et al. (2020) studied this question.
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