We compute the dynamical structure factor of the spin-½ triangular Heisenberg model using the mean-field Schwinger boson theory. We find that a reconstructed dispersion, resulting from a non-trivial redistribution of the spectral weight, agrees quite well with the spin excitation spectrum recently found with series expansions. In particular, we recover the strong renormalization with respect to linear spin wave theory along with the appearance of roton-like minima. Furthermore, near the roton-like minima the contribution of the two spinon continuum to the static structure factor is about 40% of the total weight. By computing the density-density dynamical structure factor, we identify an unphysical weak signal of the spin excitation spectrum with the relaxation of the local constraint of the Schwinger bosons at the mean-field level. Based on the accurate description obtained for the static and dynamic ground-state properties, we argue that the bosonic spinon theory should be considered seriously as a valid alternative to interpret the physics of the triangular Heisenberg model.
We investigate the spin dynamics of the square-lattice spin- Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Néel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
We compute the zero temperature dynamical structure factor
S(q,ω) of the triangular lattice Heisenberg model using a Schwinger Boson approach that includes the Gaussian fluctuations (
1/N correction) of the saddle point solution. While the ground state of this model exhibits a well-known 120
∘ magnetic ordering, the excitation spectrum revealed by
S(q,ω) has a strong quantum character that is not captured by low-order
1/S expansions. The low-energy magnons consist of two spinon bound states confined by gauge fluctuations of the auxiliary fields, which can produce internal structure of the magnon peaks. In addition, the high-energy continuum of spinon modes extends up to about three times the single-magnon bandwidth.
We investigate the spin dynamics of the square-lattice spin- 1/2 Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Neel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at (π, 0) found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.
We find that the Schwinger boson mean field theory (SBMFT) supplemented with Gutzwiller projection provides an exceedingly accurate description for the ground state of the spin-12triangular lattice antiferromagnetic Heisenberg model (spin-12TLHAF). However, we find the SBMFT fails even qualitatively in the description of the dynamical behavior of the system. In particular, the SBMFT fails to predict the Goldstone mode in the magnetic ordered phase. We show that the coherent peak in the two-spinon continuum in the presence of spinon condensate should not be interpreted as a magnon mode. The SBMFT also predicts incorrectly a gapless longitudinal spin fluctuation mode in the magnetic ordered phase. We show that these failures are related to the following facts: (1) spinon condensation fails to provide a consistent description of the order parameter manifold of the 120 degree ordered phase. (2) There lacks in the SBMFT the coupling between the uncondensed spinon and the spinon condensate, which breaks both the spin rotational and the translational symmetry. (3) There lacks in the SBMFT the rigidity that is related to the no double occupancy constraint on the spinon system. We show that such failures of the SBMFT is neither restricted to the spin-12TLHAF nor to the magnetic ordered phase. We proposed a generalized SBMFT to resolve the first two issues and a new formalism to address the third issue.
Large-
S and large-
N theories (spin value
S and spinor component number
N) are complementary, and sometimes conflicting, approaches to quantum magnetism. While large-
S spin-wave theory captures the correct semiclassical behavior, large-
N theories, on the other hand, emphasize the quantumness of spin fluctuations. In order to evaluate the possibility of the nontrivial recovery of the semiclassical magnetic excitations within a large-
N approach, we compute the large-
S limit of the dynamical spin structure factor of the triangular lattice Heisenberg antiferromagnet within a Schwinger boson spin representation. We demonstrate that, only after the incorporation of Gaussian (
1/N) corrections to the saddle-point ($N=\ensuremath{\infty}$) approximation, we are able to exactly reproduce the linear spin-wave theory results in the large-
S limit. The key observation is that the effect of
1/N corrections is to cancel out exactly the main contribution of the saddle-point solution, while the collective modes (magnons) consist of two spinon bound states arising from the poles of the random phase approximation propagator. This result implies that it is essential to consider the interaction of the spinons with the emergent gauge fields and that the magnon dispersion relation should not be identified with that of the saddle-point spinons.
The Kitaev model is an exactly solvable model that exhibits a quantum spin liquid as its ground state. While this model was originally proposed as an S = 1 / 2 spin model on a honeycomb lattice, extensions to higher-spin systems have recently attracted attention. In contrast to the S = 1 / 2 case, such higher- S models are not exactly solvable and remain poorly understood, particularly for spin excitations at finite temperatures. Here, we focus on the S = 1 Kitaev model, which has been proposed to host bosonic quasiparticles. We investigate this model using Schwinger boson mean-field theory, where bosonic spinons are introduced as fractional quasiparticles by extending bond operators to address anisotropic spin interactions. We determine the mean-field parameters that realize a quantum spin liquid in both ferromagnetic and antiferromagnetic Kitaev models. Based on this mean-field ansatz, we calculate the dynamical and equal-time spin structure factors. We find that, when one uses the conventional decoupling scheme based on Wick decoupling with respect to spinons to calculate spin correlations, the resultant spin structure factors exhibit a momentum dependence that is not consistent with the sign structure expected from the exchange interaction: They possess a strong spectral weight indicating ferromagnetic (antiferromagnetic) correlations in the antiferromagnetic (ferromagnetic) Kitaev model. To resolve this issue, we propose an alternative scheme for evaluating the spin correlations, which is based on decoupling with respect to the bond operators. We demonstrate that, in our scheme, this discrepancy is removed, and the momentum dependence of the spin structure factors is consistent with the sign of the exchange constant. We also calculate the temperature evolution of the dynamical spin structure factor and find that the continuum observed at zero temperature splits into two distinct structures as the temperature increases, which can be understood in terms of the bandwidth narrowing of spinons. Finally, we clarify the origin of why the two distinct decoupling schemes result in different momentum dependences of the spin structure factors and discuss their relationship to results obtained in previous studies.