Inspired by the recent theoretical suggestion that the random-bond
S=1/2 antiferromagnetic Heisenberg model on the triangular and the kagome lattices might exhibit a randomness-induced quantum spin liquid (QSL) behavior when the strength of the randomness exceeds a critical value, and that this ``random-singlet state'' might be relevant to the QSL behaviors experimentally observed in triangular organic salts $\ensuremath{\kappa}\text{\ensuremath{-}}{(\mathrm{ET})}_{2}{\mathrm{Cu}}_{2}{(\mathrm{CN})}_{3}\phantom{\rule{4pt}{0ex}}\mathrm{and}\phantom{\rule{4pt}{0ex}}{\mathrm{EtMe}}_{3}\mathrm{Sb}{[\mathrm{Pd}{(\mathrm{dmit})}_{2}]}_{2}$ and in kagome herbertsmithite
ZnCu3(OH)6Cl2, we further investigate the nature of the static and the dynamical spin correlations of these models. We compute the static and the dynamical spin structure factors,
S(q) and $S(\mathbf{q},\ensuremath{\omega})$, by means of an exact diagonalization method. In both triangular and kagome models, the computed $S(\mathbf{q},\ensuremath{\omega})$ in the random-singlet state depends on the wave vector
q only weakly, robustly exhibiting gapless behaviors accompanied by the broad distribution extending to higher energy $\ensuremath{\omega}$. Especially in the strongly random kagome model, $S(\mathbf{q},\ensuremath{\omega})$ hardly depends on
q, and exhibits an almost flat distribution for a wide range of $\ensuremath{\omega}$, together with a $\ensuremath{\omega}=0$ peak. These features agree semiquantitatively with the recent neutron-scattering data on a single-crystal herbertsmithite. Furthermore, the computed magnetization curve agrees almost quantitatively with the experimental one recently measured on a single-crystal herbertsmithite. These results suggest that the QSL state observed in herbertsmithite might indeed be the randomness-induced QSL state, i.e., the random-singlet state.
Experimental quest for the hypothetical "quantum spin liquid" state has recently met a few promising candidate materials including organic salts κ-(ET)2Cu2(CN)3 and EtMe3Sb[Pd(dmit)2]2, S=1/2 triangular-lattice Heisenberg antiferromagnets consisting of molecular dimers. These compounds exhibit no magnetic ordering nor the spin freezing down to very low temperature, while various physical quantities exhibit gapless behaviors. Recent dielectric measurements revealed the glassy dielectric response suggesting the random freezing of the electric polarization degrees of freedom. Inspired by this observation, we propose as a minimal model of the observed quantum spin-liquid behavior the S=1/2 antiferromagnetic Heisenberg on the triangular lattice with a quenched randomness in the exchange interaction. We study both zero- and finite-temperature properties of the model by an exact diagonalization method, to find that when the randomness exceeds a critical value the model exhibits a quantum spin-liquid ground state. This randomness-induced quantum spin-liquid state exhibits gapless behaviors including the temperature-linear specific heat. The results provide a consistent explanation of the recent experimental observations on organic salts.
We investigate the ground-state and finite-temperature properties of the bond-random
s=1/2 Heisenberg model on a honeycomb lattice with frustrated nearest- and next-nearest-neighbor antiferromagnetic interactions,
J1 and
J2, by the exact diagonalization and the Hams--de Raedt methods. The ground-state phase diagram of the model is constructed in the randomness versus the frustration (
J2/J1) plane, with the aim of clarifying the effects of randomness and frustration in stabilizing a variety of distinct phases. We find that the randomness induces the gapless quantum spin liquid (QSL)-like state, the random-singlet state, in a wide range of parameter space. The observed robustness of the random-singlet state suggests that the gapless QSL-like behaviors might be realized in a wide class of frustrated quantum magnets possessing a certain amount of randomness or inhomogeneity, without fine-tuning the interaction parameters. Possible implications to recent experiments on the honeycomb-lattice magnets Ba
3CuSb
2O
9 and 6HB-Ba
3NiSb
2O
9 exhibiting the gapless QSL-like behaviors are discussed.
A preponderance of evidence suggests that the ground state of the nearest-neighbor
S=1/2 antiferromagnetic Heisenberg model on the kagome lattice is a gapless spin liquid. Many candidate materials for the realization of this model possess in addition a Dzyaloshinskii-Moriya (DM) interaction. We study this system by tensor-network methods and deduce that a weak but finite DM interaction is required to destabilize the gapless spin-liquid state. The critical magnitude, ${D}_{c}/J\ensuremath{\simeq}0.012(2)$, lies well below the DM strength proposed in the kagome material herbertsmithite, indicating a need to reassess the apparent spin-liquid behavior reported in this system.
The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S=1/2 antiferromagnetic Heisenberg model on the kagome lattice, has defied all theoretical and numerical methods employed to date. We apply the formalism of tensor-network states, specifically the method of projected entangled simplex states, which combines infinite system size with a correct accounting for multipartite entanglement. By studying the ground-state energy, the finite magnetic order appearing at finite tensor bond dimensions, and the effects of a next-nearest-neighbor coupling, we demonstrate that the ground state is a gapless spin liquid. We discuss the comparison with other numerical studies and the physical interpretation of this result.