  We elucidate the deep connection between the PXP model, which is a standard
model of quantum many-body scars, and the AKLT Hamiltonian. Using the framework
of embedded Hamiltonians, we establish the connection between the PXP
Hamiltonian and the AKLT Hamiltonian, which clarifies the reason why the PXP
Hamiltonian has nonthermal energy eigenstates similar to the AKLT state.
Through this analysis, we find that the presence of such nonthermal energy
eigenstates reflects the symmetry in the AKLT Hamiltonian.
