  Experimental observation of coherent oscillations in a Rydberg atom chain
[Bernien et al., Nature 551, 579 (2017)] has led to the discovery of quantum
many-body scars (QMBS) which is a new paradigm for ergodicity-breaking. The
experimental findings in the Rydberg chain can be well captured by a
kinetically constrained model called the "PXP" model, which has been shown to
host the Eigenstate Thermalization Hypothesis (ETH)-violating scar states in
the middle of the spectrum. Much effort has been put into identifying similar
kinetically restricted systems that show a violation of ETH. In this work, we
study the QMBS that can arise in one such model, namely the spin-$1$ Kitaev
chain, where owing to some conserved quantities, the Hilbert space gets
fragmented into unequal disconnected subspaces. Recently, You et al. [Phys.
Rev. Research 4, 013103 (2022)] showed that the ground state sector of this
chain can be mapped exactly onto the prototypical PXP model and thus hosts
QMBSs. Here, we demonstrate that the phenomenon of scarring is also present in
other sectors, and in particular, we identify a sector that exhibits
substantially more scarring than the ground state one. We propose an initial
state and numerically demonstrate that its fidelity revivals are robust and
longer-lived than those in the PXP model.
