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 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.
Vacancy-induced local moments in quantum paramagnetic phases: An SU(N) designer Hamiltonian study
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.
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.
The doping of quantum Heisenberg antiferromagnets on the kagome lattice by nonmagnetic impurities is investigated within the framework of a generalized quantum dimer model (QDM) describing (a) the valence-bond crystal (VBC), (b) the dimer liquid, and (c) the critical region on equal footing. Following the approach by Ralko et al. [Phys. Rev. Lett. 101, 117204 (2008)] for the square and triangular lattices, we introduce the (minimal) extension of the QDM on the kagome lattice to account for spontaneous creation of mobile S=1/2 spinons at finite magnetic field. Modulations of the dimer density (at zero or finite magnetic field) and of the local field-induced magnetization in the vicinity of impurities are computed using Lanczos exact diagonalization techniques on small clusters (48 and 75 sites). The VBC is clearly revealed from its pinning by impurities, while, in the dimer liquid, crystallization around impurities involves only two neighboring dimers. We also find that a next-nearest-neighbor ferromagnetic coupling favors VBC order. Unexpectedly, a small-size spinon-impurity bound state appears in some region of the dimer-liquid phase. In contrast, in the VBC phase the spinon delocalizes within a large region around the impurity, revealing the weakness of the VBC confining potential. Lastly, we observe that an impurity concentration as small as 4% enhances dimerization substantially. These results are confronted to the valence-bond glass scenario [R. R. P. Singh, Phys. Rev. Lett. 104, 177203 (2010)] and implications to the interpretation of the nuclear magnetic resonance spectra of the Herbertsmithite compound are outlined.
We investigate the properties of the Kitaev honeycomb model with both site dilution and exchange randomness. Embarking on this work, we review disorder in some strongly correlated electron systems, including spin-½ and spin-1 Heisenberg antiferromagnetic chains, two dimensional Heisenberg antiferromagnets, the cuprates and graphene. We outline some aspects of resonating valence bond phases, valence bond solids, spin liquids and quantum computation that are pertinent to an understanding of the Kitaev model. The properties of the Kitaev model without disorder are discussed and it is found to be a critical spin liquid, with algebraic correlations in two spin operators sigma^{alpha}_{i}sigma^{alpha}_{j}, where i and j are either end of a link of type alpha = x, y or z on the honeycomb lattice. The Kitaev model is exactly solvable and we show that this remains so in the presence of site dilution and exchange randomness. We find that vacancies bind a flux. In the gapped phase, a vacancy forms an effective paramagnetic moment. With two or more vacancies we describe the interaction of their effective moments and show that a finite density of vacancies leads to a divergent macroscopic susceptibility at small fields. In the gapless phase the effective moment has a susceptibility that is, to leading order at small fields, chi(h)~log(1/h). Interaction between the moments from two vacancies on opposite sublattices cuts off this divergence in susceptibility at a large but finite constant. Two vacancies on the same sublattice behave quite differently and we find the combined susceptibility is parametrically larger than that of an isolated vacancy, chi(h)sim [h(log(1/h))^{3/2}]^{-1}. We also investigate the effects of slowly varying, quenched disorder in exchange coupling. We demonstrate that this does not qualitatively affect the susceptibility but show that the heat capacity C ~ T^{2/z}, where z is a measure of the disorder and increases from one with increasing disorder strength.
We investigate the properties of the Kitaev honeycomb model with both site dilution
and exchange randomness. Embarking on this work, we review disorder in some strongly correlated electron systems, including spin-½ and spin-1 Heisenberg antiferromagnetic chains, two dimensional Heisenberg antiferromagnets, the cuprates and graphene. We outline some aspects of resonating valence bond phases, valence bond solids, spin liquids and quantum computation that are pertinent to an understanding of the Kitaev model. The properties of the Kitaev model without disorder are discussed and it is found to be a critical spin liquid, with algebraic correlations in two spin operators sigma^{alpha}_{i}sigma^{alpha}_{j}, where i and j,/em> are either end of a link of type alpha = x, y or z on the honeycomb lattice.
The Kitaev model is exactly solvable and we show that this remains so in the presence of site dilution and exchange randomness. We find that vacancies bind a flux. In the gapped phase, a vacancy forms an effective paramagnetic moment. With two or more vacancies we describe the interaction of their effective moments and show that a finite density of vacancies leads to a divergent macroscopic susceptibility at small fields.
In the gapless phase the effective moment has a susceptibility that is, to leading order at small fields, chi(h)~log(1/h). Interaction between the moments from two vacancies on opposite sublattices cuts off this divergence in susceptibility at a large but finite constant. Two vacancies on the same sublattice behave quite differently and we find the combined susceptibility is parametrically larger than that of an isolated vacancy, chi(h)sim [h(log(1/h))^{3/2}]^{-1}.
We also investigate the effects of slowly varying, quenched disorder in exchange coupling. We demonstrate that this does not qualitatively affect the susceptibility but show that the heat capacity C ~ T^{2/z}, where z is a measure of the disorder and increases from one with increasing disorder strength.