We study a ferromagnetic XXZ Heisenberg model on a Lieb lattice. A set of exact eigenstates is constructed based on the restricted spectrum generating algebra (RSGA) when a resonant staggered magnetic field is applied. These states are identical to the eigenstates of a system of two coupled angular momenta. Furthermore, we find that the RSGA can be applied to other eigenstates of the Lieb lattice in an approximate manner. Numerical simulations reveal that there exist sets of eigenstates, which obey a quasi-RSGA. These states act as energy towers within the low-lying excited spectrum, indicating that they are quantum many-body scars. Our main results are the identification of both exact and approximate scar states and their dynamical signatures.

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• Eigenstate thermalization
• Quantum scars
• Quantum spin models
• Heisenberg model