This paper is concerned with physics of the low-energy singlet excitations found to exist below the spin gap in numerical studies of the Kagome lattice quantum Heisenberg antiferromagnet. Insight into the nature of these excitations is obtained by exploiting an approximate mapping to a fully frustrated transverse-field Ising model on the dual dice lattice. This Ising model is shown to possess at least two phases---an ordered phase that also breaks translational symmetry with a large unit cell, and a paramagnetic phase. The former is argued to be a likely candidate for the ground state of the original Kagome magnet which thereby exhibits a specific pattern of dimer ordering with a large unit cell. Comparisons with available numerical results are made.
In this paper we report the latest results of exact diagonalizations of SU (2) invariant models on various lattices (square, triangular, hexagonal, checkerboard and kagomé lattices) and revisit critically in this light some of our previous analysis. We focus on the low-lying levels in each S sector. The differences in behavior between gapless systems and gapped ones are exhibited. The plausibility of a gapless spin liquid in the Heisenberg model on the kagomé lattice is discussed. A rough estimate of the spin susceptibility in such an hypothesis is given. The evolution of the intra- S -channel spectra under the effect of a small perturbation is consistent with the proximity of a quantum critical point. We reemphasize that the very small intra- S -channel energy scale observed in exact spectra is a very interesting information to understand the low- T dynamics of this model.
We study a Heisenberg antiferromagnet (AF) on a one-dimensional strip composed of two rows of corner sharing triangular plaquettes. The geometry of this ladder-like lattice naturally allows for two different exchange couplings, one between pairs of spins on the outer legs (J) and a different one between the spins on the axis and their nearest neighbors on the legs ${(J}^{\ensuremath{'}}).$ For ${J/J}^{\ensuremath{'}}\ensuremath{\lesssim}0.5$ the model is a ferrimagnet. Our main interest is in the region ${J/J}^{\ensuremath{'}}\ensuremath{\gtrsim}0.5,$ where the classical ground state of this system shows the same macroscopic degeneracy as the classical ground state of the antiferromagnet on the kagom\'e lattice. To explore to which extent this similarity between the classical ground states of these two models carries over to their quantum states we have applied exact diagonalization techniques and density-matrix renormalization group (DMRG) methods to our model. Exact diagonalization is restricted to system sizes of up to
N=30 sites. For ${J/J}^{\ensuremath{'}}=1,$ the results obtained by this technique, low-energy spectra, correlation functions and the specific heat, agree qualitatively with the results obtained for finite samples of the kagom\'e AF. As in the case of the kagom\'e AF, these finite size results suggest that our model is a spin liquid with a gap between the ground state and the lowest spin excitation. However, extrapolations from DMRG data for strips of up to
N=120 sites point towards a vanishing spin gap in a wide range of couplings, $0.5\ensuremath{\lesssim}{J/J}^{\ensuremath{'}}\ensuremath{\lesssim}1.25,$ so that contrary to the above conjecture, our one-dimensional model may in fact be critical in this parameter range. Moreover, our DMRG data indicate that the model undergoes a transition to a gapped state as the ratio ${J/J}^{\ensuremath{'}}$ increases through the value ${J/J}^{\ensuremath{'}}\ensuremath{\simeq}1.25.$ In the vicinity of the transition point, a high density of low-lying singlets develops in the spin gap.
There is growing evidence from both experiment and numerical studies that low half-odd integer quantum spins on a kagome lattice with predominant antiferromagnetic near-neighbor interactions do not order magnetically or break lattice symmetries even at temperatures much lower than the exchange interaction strength. Moreover, there appears to be a plethora of low-energy excitations, predominantly singlets but also spin carrying, which suggests that the putative underlying quantum spin liquid is a gapless ``critical spin liquid'' rather than a gapped spin liquid with topological order. Here, we develop an effective field theory approach for the spin-
21 Heisenberg model with easy-plane anisotropy on the kagome lattice. By employing a vortex duality transformation, followed by a fermionization and flux smearing, we obtain access to a gapless yet stable critical spin liquid phase, which is described by
(2+1)-dimensional quantum electrodynamics
(QED3) with an emergent SU(8) flavor symmetry. The specific heat, thermal conductivity, and dynamical structure factor are extracted from the effective field theory, and contrasted with other theoretical approaches to the kagome antiferromagnet.
We analyse the antiferromagnetic spin-1/2 Heisenberg model on a depleted kagome lattice, where some bonds have been reduced to exchange integral J_2 << J_1. The fully depleted system consists of 1D chains, each with a doubly degenerate singlet-pair ground state and a spectral gap (like the Majumdar-Ghosh model). There are localised and itinerant low-energy excitations. The modes from the lowest branch of excitations are incapable of lifting the 2D system's ground state degeneracy at finite J_2/J_1 << 1. Low-energy excitations of the 2D system are dominated by coherently propagating bound states of the 1D excitations.
Due to strong geometric frustration and quantum fluctuation, the
S=1/2 quantum Heisenberg antiferromagnet on the
kagome lattice has long been considered as an ideal platform to realize a spin liquid (SL), a phase exhibiting fractionalized excitations without any symmetry breaking. A recent numerical study (Yan et al., e-print arXiv:1011.6114) of the Heisenberg
S=1/2,kagome lattice model (HKLM) shows, in contrast to earlier results, that the ground state is a singlet-gapped SL with signatures of
Z2 topological order. Motivated by this numerical discovery, we use the projective symmetry group to classify all 20 possible Schwinger fermion mean-field states of
Z2 SLs on the
kagome lattice. Among them we found only one gapped
Z2 SL (which we call the ${\mathbb{Z}}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ state) in the neighborhood of the U(1) Dirac SL state. Since its parent state, i.e., the U(1) Dirac SL, was found [Ran et al., Phys. Rev. Lett. 98, 117205 (2007)] to be the lowest among many other candidate U(1) SLs, including the uniform resonating-valence-bond states, we propose this ${\mathbb{Z}}_{2}[0,\ensuremath{\pi}]\ensuremath{\beta}$ state to be the numerically discovered SL ground state of the HKLM.