Quantum many-body scars in the Bose-Hubbard model with strong three-body losses*

We find the exact athermal eigenstates in the Bose-Hubbard (BH) model with strong three-body losses, based on the construction of quantum many-body scar (QMBS) states in the S=1 XY model. These states appear by applying an SU(2) ladder operator, formed by a linear combination of two-particle annihilation operators, to the fully occupied state. Through the refined Holstein-Primakoff expansion, we elucidate that the QMBS states in the S=1 XY model are equivalent to those in the constrained BH model, augmented by additional correlated hopping terms. Furthermore, in the strong coupling limit of the constrained BH model, the QMBS state emerges as the lowest-energy eigenstate of the effective model within the highest-energy sector. This observation allows us to prepare QMBS states through some adiabatic process, thereby paving the way for their realization in ultracold-atom experiments.