We study the Hilbert space fragmentation (HSF) in hardcore Bose and Fermi Hubbard models in the framework of the restricted spectrum generating algebra (RSGA). We present a family of hardcore Bose-Hubbard models with repulsive density-density interactions on a generalized Lieb lattice. We show that this system possesses the RSGA structure in the large interaction strength limit, exhibiting quantum HSF. It allows us to construct a set of exact condensate eigenstates, possessing off-diagonal long-range order. Based on numerical simulations conducted on several representative lattices, we demonstrate the existence of weak fragmentations when the constraints are not exact. As applications, we also studied the connection between HSF and RSGA in modified fermionic Hubbard models, where the $\eta$-pairing states are shown to be energy towers, acting as quantum scars.

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• Eigenstate thermalization
• Hard-core bosons
• Magnetism
• Superconductivity
• Superfluidity
• Fermionic condensates
• Quantum many-body systems
• Strongly correlated systems
• Exact solutions for many-body systems
• Hubbard model