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Quantum scars are non-thermal eigenstates characterized by low entanglemententropy, initially detected in systems subject to nearest-neighbor Rydbergblockade, the so called PXP model. While most of these special eigenstateselude an analytical description and seem to hybridize with nearby thermaleigenstates for large systems, some of them can be written as matrix productstates (MPS) with size-independent bond dimension. We study the response ofthese exact quantum scars to perturbations by analysing the scaling of thefidelity susceptibility with system size. We find that some of them areanomalously stable at first order in perturbation theory, in sharp contrast tothe eigenstate thermalization hypothesis. However, this stability seems tobreakdown when all orders are taken into account. We further investigate modelswith larger blockade radius and find a novel set of exact quantum scars, thatwe write down analytically and compare with the PXP exact eigenstates. We showthat they exhibit the same robustness against perturbations at first order.

Exact many-body scars and their stability in constrained quantum chains