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Physical review. B, Condensed matter

Dynamics of the two-dimensional spin-1/2Heisenberg antiferromagnet: Exact results versus Schwinger-boson mean-field theory

C.-X. Chen, H.-B. Schüttler

Published Jul 1, 1989• 32 citations
Publisher

Abstract

We present the first exact results for the T=0 dynamical structure factor of finite-sized two-dimensional square-lattice spin-(1/2 antiferromagnetic Heisenberg systems with up to 16 spins. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra at all allowed wave vectors and for all system sizes studied. We also determine the mean-field value for the T=0 staggered magnetization, ${m}^{\mathrm{MF}=0.306}$, to be in excellent agreement with published Monte Carlo results.

DOI
10.1103/physrevb.40.239

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We present the first exact results for the T=0 dynamical structure factor of finite-sized two-dimensional square-lattice spin-(1/2 antiferromagnetic Heisenberg systems with up to 16 spins. Our results are compared to a recently proposed Schwinger boson mean-field theory. We find that the mean-field theory represents an excellent approximation to the exact spin excitation spectra at all allowed wave vectors and for all system sizes studied. We also determine the mean-field value for the T=0 staggered magnetization, mMF=0.306{m}^{\mathrm{MF}=0.306}mMF=0.306, to be in excellent agreement with published Monte Carlo results.
A generalized Schwinger boson representation is proposed to describe the two-dimensional SU(4) symmetric spin-orbital quantum antiferromagnet. A uniform mean field solution gives rise to an antiferromagnetic long range ordered state with a small staggered magnetization ms=0.07566m_{s}=0.07566ms​=0.07566, and the recent quantum Monte Carlo simulations on rather large lattice sizes have provided strong evidence to support these mean field results.
We discuss recent applications of exact numerical continued fraction expansion (CFE) techniques to calculate dynamical correlation functions of various strong-coupling models related to the high-temperature cuprate superconductors. For the two-dimensional square-lattice spin-1/2 Heisenberg antiferromagnet, we present exact results for the zero-temperature dynamical structure factor on finite-sized lattices and compare them to approximate results from a Schwinger boson mean-field theory, recently proposed by Arovas and Auerbach. We find that the mean-field theory represents a very good approximation to the exact spin excitation spectra and to the static spin correlations. We then investigation the dynamical spin-spin structure factor and the single-particle spectral function for finite model clusters with dopant induced hole-type charge carriers, in the strong-coupling limit of both the single-band Hubbard model (t-J-model) and the three-band Hubbard model (Kondo-Heisenberg model). Our results are consistent with the physical picture recently proposed by Zhang and Rice which implies an approximate mapping of the low-energy states in the three-band model onto an effective single-band theory. 33 refs., 4 figs.
We investigate the zero-temperature and the finite-temperature properties of the two-dimensional antiferromagnetic quantum spin system composed of the s=1/2s=1/2s=1/2 and s=1s=1s=1 spins. The spin excitation spectrum as well as the thermodynamic quantities are computed by means of the Schwinger-boson mean-field theory. We discuss how the magnetic double structure with the gapful and the gapless excitations is generated, and apply the results systematically to the Haldane gap system in a staggered magnetic field and also to the weakly coupled ferrimagnetic mixed-spin chains. It is confirmed that the results obtained are consistent with the experiments for the quasi-one-dimensional Haldane compounds R2BaNiO5.{R}_{2}{\mathrm{BaNiO}}_{5}.R2​BaNiO5​.
We find the corrections to the conventional 1/S expansion for the spin-wave velocity in the two-dimensional S=1/2 Heisenberg antiferromagnet. We do this by solving exactly for the ground and excited states of small clusters of up to 25 spins. We use open boundary conditions with a staggered Weiss effective field consistent with the correct quantum Monte Carlo staggered magnetization MS{\mathit{M}}_{\mathit{S}}MS​=0.31. The numerical results are directly compared with the 1/S expansion for the same clusters. The exact spin-wave velocity is given by c=Z1.158 \ensuremath{\surd}2 Ja, where Z is within 2% of unity. Our best estimate gives Z\ensuremath{\approxeq}1.006.
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 investigate the quantum dynamics of the spins on different Heisenberg antiferromagnetic spin lattice systems. Firstly, we applied the coupled-cluster method to the spin-1/2 antiferromagnetic \emph{XXZ} model on a square lattice by employing an approximation which contains two-body long-range correlations and high-order four-body local correlations. Improvement is found for the ground-state energy, sublattice magnetization, and the critical anisotropy when comparing with the approximation including the two-body correlations alone. We also obtain the full excitation spectrum which is in good agreement with the quantum Monte Carlo results and the high-order spin-wave theory.Secondly, we study the longitudinal excitations of quantum antiferromagnets on a triangular lattice by a recently proposed microscopic many-body approach based on magnon-density waves. We calculate the full longitudinal excitation spectra of the antiferromagnetic Heisenberg model for a general spin quantum number in the isotropic limit. Similar to the square lattice model, we find that, at the center of the first hexagonal Brillouin zone Γ(q=0)\Gamma(\mathbf q=0)Γ(q=0) and at the magnetic ordering wavevectors ±[Q=(4π/3,0)]\pm[\mathbf Q= (4\pi/3,0)]±[Q=(4π/3,0)], the excitation spectra become gapless in the thermodynamic limit, due to the slow, logarithmic divergence of the structure factor. However, these longitudinal modes on two-dimensional models may be considered as quasi-gapped, as any finite-size effect or small anisotropy will induce a large energy gap, when compared with the counterpart of the transverse spin-wave excitations. We have also investigated the excited states of the quasi-one-dimensional quantum antiferromagnets on hexagonal lattices, including the longitudinal modes based on the magnon-density waves. A model Hamiltonian with a uniaxial single-ion anisotropy is first studied by a spin-wave theory based on the one-boson method; the ground state thus obtained is employed for the study of the longitudinal modes. The full energy spectra of both the transverse modes (i.e., magnons) and the longitudinal modes are obtained as functions of the nearest-neighbor coupling and the anisotropy constants. We have found two longitudinal modes due to the non-collinear nature of the triangular antiferromagnetic order, similar to that of the phenomenological field theory approach by Affleck. The excitation energy gaps due to the anisotropy and the energy gaps of the longitudinal modes without anisotropy are then investigated. We then compares our results for the longitudinal energy gaps at the magnetic wavevectors with the experimental results for several antiferromagnetic compounds with both integer and non-integer spin quantum numbers, and we find good agreements after the higher-order contributions are included in our calculations.