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arXiv:2602.24203

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

Md Zahid Ansari, Souvik Kundu, Kedar Damle

Published Feb 27, 2026• 0 citations
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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.

DOI
10.48550/arxiv.2602.24203

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Vacancy-induced local moments in quantum paramagnetic phases: An SU(NNN) designer Hamiltonian study
We explore the effects of non-magnetic impurities (vacancy disorder) on the quantum paramagnetic phases stabilized by SU(NNN) designer Hamiltonians on bipartite lattices. Using the results of our quantum Monte Carlo simulations, we demonstrate that isolated vacancies seed emergent spin S=1/2S=1/2S=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.
We study the effect of a small density n_{v} of quenched nonmagnetic impurities, i.e., vacancy disorder, in gapped short-range resonating valence bond (RVB) spin liquid states and valence bond solid (VBS) states of quantum magnets. We argue that a large class of short-range RVB liquids are stable to vacancy disorder at small n_{v} on the kagome lattice, while the corresponding states on triangular, square, and honeycomb lattices are unstable to vacancy disorder at any nonzero n_{v} due to the presence of emergent vacancy-induced local moments. In contrast, VBS states are argued to be generically unstable (independent of lattice geometry) to vacancy disorder at any nonzero n_{v} due to such a local-moment instability. Our arguments rely in part on an analysis of the statistical mechanics of maximally packed dimer covers of the diluted lattice, and are fully supported by our computational results on O(N) symmetric designer Hamiltonians. These arguments also imply that short-range RVB spin liquid states are generically unstable to bond dilution on all these lattices.
We analyze the effect of quenched disorder on spin-1/2 quantum magnets in which magnetic frustration promotes the formation of local singlets. Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids. We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1/2 moments. This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations. Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1/2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate. Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1/2 per statistical unit cell. These conjectures are supported by an argument for 1D spin chains. We apply insights from this study to the phenomenology of YbMgGaO_{4}, a recently discovered triangular lattice spin-1/2 insulator which was proposed to be a quantum spin liquid. We instead explore a description based on the present theory. Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO_{4} and related materials.
We analyze the effect of quenched disorder on spin-1=2 quantum magnets in which magnetic frustration promotes the formation of local singlets.Our results include a theory for 2D valence-bond solids subject to weak bond randomness, as well as extensions to stronger disorder regimes where we make connections with quantum spin liquids.We find, on various lattices, that the destruction of a valence-bond solid phase by weak quenched disorder leads inevitably to the nucleation of topological defects carrying spin-1=2 moments.This renormalizes the lattice into a strongly random spin network with interesting low-energy excitations.Similarly, when short-ranged valence bonds would be pinned by stronger disorder, we find that this putative glass is unstable to defects that carry spin-1=2 magnetic moments, and whose residual interactions decide the ultimate low-energy fate.Motivated by these results we conjecture Lieb-Schultz-Mattis-like restrictions on ground states for disordered magnets with spin 1=2 per statistical unit cell.These conjectures are supported by an argument for 1D spin chains.We apply insights from this study to the phenomenology of YbMgGaO 4 , a recently discovered triangular lattice spin-1=2 insulator which was proposed to be a quantum spin liquid.We instead explore a description based on the present theory.Experimental signatures, including unusual specific heat, thermal conductivity, and dynamical structure factor, and their behavior in a magnetic field, are predicted from the theory, and compare favorably with existing measurements on YbMgGaO 4 and related materials.
We exhibit an exactly solvable example of a SU(2) symmetric Majorana spin liquid phase, in which quenched disorder leads to random-singlet phenomenology of emergent magnetic moments. More precisely, we argue that a strong-disorder fixed point controls the low temperature susceptibility χ(T) of an exactly solvable S=1/2 model on the decorated honeycomb lattice with vacancy and/or bond disorder, leading to χ(T)=C/T+DT^{α(T)-1}, where α(T)→0 slowly as the temperature T→0. The first term is a Curie tail that represents the emergent response of vacancy-induced spin textures spread over many unit cells: it is an intrinsic feature of the site-diluted system, rather than an extraneous effect arising from isolated free spins. The second term, common to both vacancy and bond disorder [with different α(T) in the two cases] is the response of a random singlet phase, familiar from random antiferromagnetic spin chains and the analogous regime in phosphorus-doped silicon (Si:P).
The quantum nature of electrons emerges in various exotic ways when they are put together with quantum many-body interactions. In Mott insulating systems with strong electron correlation, frustration and strong quantum fluctuations promote localized electron spins to form nontrivial quantum paramagnetic phases such as quantum spin liquid and valence bond solid preventing the development of conventional magnetic orders. In this thesis, we study such exotic quantum phases in various different frustrated quantum magnets. First, encouraged by the spin liquid phenomenology observed in Ba3XSb2O9 (X=Cu, Ni), we investigate Z2 spin liquids on a three dimensional triangular lattice by employing the Schwinger boson mean-field theory with projective symmetry group analysis. It is found that a nematic spin liquid is energetically favorable on this lattice structure rather than symmetric spin liquids. Next, we study various valence bond solid phases that can appear in kagome lattice antiferromagnets by generalizing the recently proposed phenomenological Z2 gauge theory for the topological Z2 spin liquid state found in the nearest-neighbor kagome lattice Heisenberg model. This work provides a bridge between the topological spin liquid and valence bond solid phases previously proposed for kagome lattice antiferromagnets via vison condensation in the gauge theory. Then, we consider optical conductivity in Mott insulators as an experimental probe to detect quantum paramagnetic phases like valence bond solid. Applying this idea to deformed kagome lattice antiferromagnet Rb2Cu3SnF12 with a 12-site valence bond solid state, we estimate the size of optical conductivity in this quantum magnet. After this, another quantum paramagnet BiCu2PO6 is carefully investigated to clarify its puzzling ground state nature and quasiparticle excitations. Utilizing recent high resolution neutron scattering data, we construct a microscopic spin model and also an effective theory for the low energy spin excitations in the compound. We find significant influences of magnetic anisotropies on the ground state and quasiparticle dynamics. Lastly, we investigate emergent quantum phases in the thin film geometries of the pyrochlore iridates, where a number of exotic quantum ground states are proposed to occur in bulk materials as a result of the interplay between electron correlation and strong spin-orbit coupling. The fate of these bulk phases, as well as the novel quantum states that may arise only in a thin film setting, are studied via a theoretical model that allows layer-dependent magnetic structures.
The large-N limit of a nearest-neighbor SU(N) antiferromagnet on a bipartite lattice exhibits in dimensions d\ensuremath{\ge}2 a zero-temperature phase transition between a N\'eel ordered state and a resonating-valence-bond state. Here it is shown in d=1,2 that topological effects produce spin-Peierls or valence-bond-solid order in the non-N\'eel phase with a ground-state degeneracy which varies periodically with ``spin'' for fixed N with periodicity given by the coordination number of the lattice. Thus a non-N\'eel phase of the spin-(1/2 Heisenberg model on a square lattice would be a spin-Peierls state with a fourfold degeneracy due to broken lattice rotational symmetry.