Resonant Fields Inducing Energy Towers in Lieb Quantum Spin Lattice

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.