We explore the effects of nonmagnetic impurities (vacancy disorder) on the quantum paramagnetic phases stabilized by SU($N$) designer Hamiltonians on bipartite lattices. Using the results of our quantum Monte Carlo simulations, we demonstrate that isolated vacancies seed emergent localized SU($N$) moments (analogs of spin moments for SU(2)) in their vicinity when the low-temperature state has valence bond solid order. Indeed, our quantum Monte Carlo results for the low-temperature susceptibility in such regimes show clear evidence of the vacancy-induced Curie tails associated with these emergent moments, and our zero-temperature projector Monte Carlo results on the ground-state wave function in the valence bond basis provide additional evidence in support of this picture. Further, for such designer Hamiltonians on the Lieb lattice with two additional sites on each bond of a square lattice, we identify a low-temperature spin-liquidlike regime with no sign of spin or valence bond order. This liquidlike regime serves as a testbed for validating a recently developed argument concerning the effects of vacancy disorder in such low-temperature regimes. Consistent with this argument, we find that isolated vacancies do not seed emergent local moments in such spin liquids. Instead, in the presence of vacancy disorder, emergent local moments are associated with the presence of monomers in maximum-density dimer packings of the corresponding diluted lattice.

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• Frustrated magnetism
• Impurities
• Disordered systems
• Quantum Monte Carlo