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.
Abstract Spin-1/2 kagome antiferromagnets are leading candidates for realizing quantum spin liquid (QSL) ground states. While QSL ground states are predicted for the pure Heisenberg model, understanding the robustness of the QSL to additional interactions that may be present in real materials is a forefront question in the field. Here we employ large-scale density-matrix renormalization group simulations to investigate the effects of next-nearest neighbor exchange couplings J 2 and Dzyaloshinskii-Moriya interactions D , which are relevant to understanding the prototypical kagome materials herbertsmithite and Zn-barlowite. By utilizing clusters as large as XC12 and extrapolating the results to the thermodynamic limit, we precisely delineate the scope of the QSL phase, which remains robust across an expanded parameter range of J 2 and D . Direct comparison of the simulated static and dynamic spin structure factors with inelastic neutron scattering reveals the parameter space of the Hamiltonians for herbertsmithite and Zn-barlowite, and, importantly, provides compelling evidence that both materials exist within the QSL phase. These results establish a powerful convergence of theory and experiment in this most elusive state of matter.
We use the density matrix renormalization group to perform accurate calculations of the ground state of the nearest-neighbor quantum spin S = 1/2 Heisenberg antiferromagnet on the kagome lattice. We study this model on numerous long cylinders with circumferences up to 12 lattice spacings. Through a combination of very-low-energy and small finite-size effects, our results provide strong evidence that, for the infinite two-dimensional system, the ground state of this model is a fully gapped spin liquid.
In recent work, we argued that a particular algebraic spin liquid (ASL) may be the ground state of the
S=1/2 kagome lattice Heisenberg antiferromagnet. Furthermore, this state, which lacks a spin gap, is appealing in light of recent experiments on herbertsmithite
[ZnCu3(OH)6Cl2]. Here, we study the properties of this ASL in more detail using both the low-energy effective field theory and Gutzwiller-projected wave functions of fermionic spinons. We identify the competing orders of the ASL, which are observables having slowly decaying power-law correlations---among them we find a set of magnetic orders lying at the
M points of the Brillouin zone, the familiar $\mathbit{q}=0$ magnetic ordered state, the ``Hastings'' valence-bond solid (VBS) state, and a pattern of vector spin-chirality ordering corresponding to one of the Dzyaloshinskii--Moriya (DM) interaction terms present in herbertsmithite. Identification of some of these orders requires an understanding of the quantum numbers of magnetic monopole operators in the ASL. We discuss the detection of the magnetic and VBS competing orders in experiments. While we primarily focus on a clean system without DM interaction, we consider the effects of small DM interaction and argue that, surprisingly, it leads to spontaneously broken time-reversal symmetry (for DM interaction that preserves
XY spin rotation symmetry, there is also
XY magnetic order). Our analysis of the projected wave function provides an estimate of the ``Fermi velocity''
vF that characterizes all low-energy excitations of the ASL---this allows us to estimate the specific heat, which compares favorably with experiments. We also study the spin and bond correlations of the projected wave function and compare these results with those of the effective field theory. While the spin correlations in the effective field theory and wave function seem to match rather well (although not completely), the bond correlations are more puzzling. We conclude with a discussion of experiments in herbertsmithite and make several predictions.
It has been suggested that the nearest-neighbor antiferromagnetic Heisenberg model on the Kagome lattice may be a good starting point for understanding the spin-liquid behavior discovered in herbertsmithite. In this work, we investigate possible quantum spin liquid phases in the presence of spin-rotation symmetry-breaking perturbations such as Dzyaloshinskii-Moriya and Ising interactions, as well as second-neighbor antiferromagnetic Heisenberg interactions. Experiments suggest that such perturbations are likely to be present in herbertsmithite. We use the projective symmetry group analysis within the framework of the slave-fermion construction of quantum spin liquid phases and systematically classify possible spin liquid phases in the presence of perturbations mentioned above. The dynamical spin-structure factor for relevant spin liquid phases is computed and the effect of those perturbations are studied. Our calculations reveal dispersive features in the spin structure factor embedded in a generally diffuse background due to the existence of fractionalized spin-
1/2 excitations called spinons. For two of the previously proposed
Z2 states, the dispersive features are almost absent, and diffuse scattering dominates over a large energy window throughout the Brillouin zone. This resembles the structure factor observed in recent inelastic neutron-scattering experiments on singlet crystals of herbertsmithite. Furthermore, one of the
Z2 states with the spin structure factor with mostly diffuse scattering is gapped, and it may be adiabatically connected to the gapped spin liquid state observed in recent density-matrix renormalization group calculations for the nearest-neighbor antiferromagnetic Heisenberg model. The perturbations mentioned above are found to enhance the diffuse nature of the spin structure factor and reduce the momentum dependencies of the spin gap. We also calculate the electron spin resonance (ESR) absorption spectra that further characterize the role of spin-rotation symmetry-breaking perturbations in these states. We suggest that the measurement of ESR spectra can shed more light into the nature of the ground state in herbertsmithite.
The defining problem in frustrated quantum magnetism, the ground state of the nearest-neighbor S ¼ 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.