We uncover the exact athermal eigenstates in the Bose-Hubbard (BH) model with a three-body constraint, motivated by the exact construction of quantum many-body scar (QMBS) states in the $S=1$ $XY$ model. These states are generated by applying an $\mathrm{SU}\left(2\right)$ ladder operator consisting of a linear combination of two-particle annihilation operators to the fully occupied state. By using the improved Holstein-Primakoff expansion, we clarify that the QMBS states in the $S=1$ $XY$ model are equivalent to those in the constrained BH model with additional correlated hopping terms. We also find that, in the strong-coupling limit of the constrained BH model, the QMBS state exists as the lowest-energy eigenstate of the effective model in the highest-energy sector. This fact enables us to prepare the QMBS states in a certain adiabatic process and opens up the possibility of observing them in ultracold-atom experiments.

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• Bose gases
• Cold atoms & matter waves
• Cold gases in optical lattices
• Eigenstate thermalization
• Nonequilibrium statistical mechanics
• Quantum scars
• Quantum simulation
• Atomic gases
• Bose-Hubbard model
• Exact diagonalization