Vacancy-induced local moments in quantum paramagnetic phases: An SU($N$) designer Hamiltonian study

TL;DR

This study investigates how non-magnetic vacancies influence quantum paramagnetic phases in SU(N) Hamiltonians, revealing vacancy-induced local moments in ordered phases but not in spin liquids, using quantum Monte Carlo simulations.

Contribution

It demonstrates that vacancies induce local moments in valence bond solid phases but not in spin liquids, providing new insights into impurity effects in quantum magnetic systems.

Findings

Vacancies induce local moments in valence bond solid phases.

No local moments are induced in spin liquid regimes by vacancies.

Emergent moments in spin liquids relate to monomers in dimer packings.

Abstract

We explore the effects of non-magnetic 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 spin $S=1/2$ moments 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 shows 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 wavefunction 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 liquid-like regime with no sign of spin or valence bond order. This liquid-like regime serves as a test bed 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.