Depictions of the interactions included in the quantum spin model studied in this work. The nearest-neighbor Heisenberg exchange (J) interactions act on all bonds on the square lattice drawn in black here. The different arrangements of the n singlet projectors (n = 3, 4) in the multi-projector product terms are columnar n = 3 of strength Q_3C in (a), staggered n = 3 of strength Q_3S in (b), and n = 4 with a larger separation of the projectors in (c) with strength Q_4H. The Hamiltonian contains all spacial translations of the projectors so that the full square-lattice symmetry is maintained.