We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the
S=1 Heisenberg antiferromagnet with easy-axis or easy-plane single-site anisotropy on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared to spin-wave theory.
In this paper we have applied the coupled-cluster method to investigate the ground state of the spin-1 Heisenberg antiferromagnet with anisotropic exchange interaction and easy-plane single-ion anisotropy. A coupled-cluster approximation up to the second level has been performed to evaluate the ground-state energy and staggered magnetization for various lattices such as linear chain, honeycomb, square, simple cubic, and body-centered-cubic lattice. The convergence of our results is fairly rapid, and thus the coupled-cluster method seems to be a practical tool for calculating ground-state energy of a spin system since only the first few levels of approximation will be needed in actual practice.
We calculate ground state properties (energy, magnetization, susceptibility) and one-particle spectra for the
S=1 Heisenberg antiferromagnet with easy-axis or easy-plane single site anisotropy, on the square lattice. Series expansions are used, in each of three phases of the system, to obtain systematic and accurate results. The location of the quantum phase transition in the easy-plane sector is determined. The results are compared with spin-wave theory.
We use the Schwinger boson mean-field theory, in which the constraint is imposed on the average, to the quantum Heisenberg antiferromagnetic chain with single-ion anisotropy (D > 0). Under the mean-field approximation to decouple the biquadratic term by introducing two HS fields and take the short range correlation and the coupling of on-site bosons into account, we find a clear and direct description for this system, and get two excitation spectra at T = 0 K, which distinguish the sz = 0 singlet and sz = ± 1 doublet. We also see that the relative phase of the two HS fields, having the lowest energy, is the one equal to zero.
Results of exact numerical work on the spectra and thermodynamic properties are presented for finite clusters in one and two dimensions, for the isotropic Heisenberg Hamiltonian and the Heisenberg Hamiltonian with longitudinal anisotropy. Eigenvalues of the isotropic Heisenberg loops (that is, those with periodic boundary conditions) of $N\ensuremath{\le}12, 8, 6, 5$, 5 particles, each of spin \textonehalf{}, 1,
23, 2 and
25, respectively, are found. It is shown that the spin-
S linear chain ($N\ensuremath{\rightarrow}\ensuremath{\infty}$) will have ground-state energy per spin $\frac{{\ensuremath{\epsilon}}_{\ensuremath{\infty}}^{s}}{2J}=\ensuremath{-}1.404\ifmmode\pm\else\textpm\fi{}0.002, \ensuremath{-}2.85\ifmmode\pm\else\textpm\fi{}0.03, \ensuremath{-}4.7\ifmmode\pm\else\textpm\fi{}0.4 \mathrm{and} \ensuremath{-}7.1\ifmmode\pm\else\textpm\fi{}0.5$, for
S=1,23,2,and25, respectively. For antiferromagnetic interaction, the lowest excited states of the loops with even number of particles have spin 1 and the familiar double sine spectrum; while for the spin-\textonehalf{} case the eigenvalues are very different from the result of the spin-wave theory, they approach this limit as the spin increases, and for spin
25, the infinite-spin results of the spin-wave theory should be quite accurate. For ferromagnetic loops, there exist spin-wave bound states for higher spins just like those familiar in the spin-\textonehalf{} linear chain. Effective magnetic moments for these loops are tabulated. We also present the moments for the
N=8 spin-\textonehalf{} chain (with open ends), and find the difference to be small. Results on the 3\ifmmode\times\else\texttimes\fi{}4 two-dimensional Heisenberg antiferromagnet are presented and compared with experimental data. Finally, we show some examples of the violation of the nondegeneracy rule, similar to those found by Heilmann and Lieb; levels belonging to different representations of a symmetry group remain permanently degenerate when a parameter is varied.
The
S=1 bilinear-biquadratic Heisenberg exchange model on the triangular lattice with a single-ion anisotropy has previously been shown to host a number of exotic magnetic and nematic orders [Moreno-Cardoner et al., Phys. Rev. B 90, 144409 (2014)], including an extensive region of ``supersolid'' order. In this work, we amend the model by an
XXZ anisotropy in the exchange interactions. Tuning to the limit of an exactly solvable
S=1 generalized Ising-/Blume-Capel-type model provides a controlled limit to access phases at finite transverse exchange. Notably, we find an additional macroscopically degenerate region in the phase diagram and study its fate under perturbation theory. We further map out phase diagrams as a function of the
XXZ anisotropy parameter, the ratio of bilinear and biquadratic interactions, and single-ion anisotropy, and we compute corrections to the total ordered moment in various phases using systematically constructed linear flavor-wave theory. We also present linear flavor-wave spectra of various states, finding that the lowest-energy band in three-sublattice generalized (i.e., with ${S}^{z}=\ifmmode\pm\else\textpm\fi{}1,0)$ Ising/Blume-Capel states, stabilized by strong exchange anisotropies, is remarkably flat, opening up the way to flat-band engineering of magnetic excitation via stabilizing nontrivial Ising-ordered ground states.