We discuss the spin-
21J1−−J2 model on the triangular lattice using recently proposed bond-operator theory (BOT). In agreement with previous discussions of this system, we obtain four phases upon
J2 increasing: the phase with ${120}^{\ensuremath{\circ}}$ ordering of three sublattices, the spin-liquid phase, the state with the collinear stripe order, and the spiral phase. The ${120}^{\ensuremath{\circ}}$ and the stripe phases are discussed in detail. All calculated static characteristics of the model are in good agreement with previous numerical findings. In the ${120}^{\ensuremath{\circ}}$ phase, we observe the evolution of the quasiparticles' spectra and dynamical structure factors (DSFs) upon approaching the spin-liquid phase. Some of the considered elementary excitations were introduced first in our recent study of this system at
J2=0 using the BOT. In the stripe phase, we observe that the doubly degenerate magnon spectrum known from the spin-wave theory (SWT) is split by quantum fluctuations, which are taken into account more accurately in the BOT. As compared with other known findings of the SWT in the stripe state, we observe additional spin-1 and spin-0 quasiparticles which give visible anomalies in the transverse and longitudinal DSFs. We obtain also a special spin-0 quasiparticle named the singlon that produces a peak only in the four-spin correlator and which is invisible in the longitudinal DSF. We show that the singlon spectrum lies below energies of all spin-0 and spin-1 excitations in some parts of the Brillouin zone. The singlon spectrum at zero momentum can be probed by the Raman scattering.
We discuss spin-
21 Heisenberg antiferromagnet on simple square lattice in magnetic field
H using a recently proposed bond-operator technique. It is well known that magnetically ordered phases of quantum magnets are well described at least qualitatively by the conventional spin-wave theory that only introduces quantum corrections into the classical solution of the problem. We observe that quantum fluctuations change drastically dynamical properties of the considered model at
H close to its saturation value: the dynamical structure factor shows anomalies corresponding to Green's function poles which have no counterparts in the spin-wave theory. That is, quantum fluctuations produce multiple short-wavelength magnon modes not changing qualitatively the long-wavelength spin dynamics. Our results are in agreement with previous quantum Monte Carlo simulations and exact diagonalization of finite clusters.
We present a bond-operator theory (BOT) suitable for the description of both magnetically ordered phases and paramagnetic phases with singlet ground states in spin-1/2 magnets. This technique allows one to trace the evolution of quasiparticles across the transition between the phases. Some elementary excitations described in the theory by separate bosons appear in conventional approaches as bound states of well-known quasiparticles (magnons or triplons). The proposed BOT provides a regular expansion of physical quantities in powers of
1/n, where
n is the maximum number of bosons that can occupy a unit cell (physical results correspond to
n=1). Two variants of BOT are suggested: for two and for four spins in the unit cell (two-spin and four-spin BOTs, respectively). We consider spin-1/2 Heisenberg antiferromagnets (HAF) on a simple square lattice bilayer by the two-spin BOT. The ground-state energy
E, the staggered magnetization
M, and quasiparticle spectra found within the first order in
1/n are in good quantitative agreement with previous results both in paramagnetic and in ordered phases not very close to the quantum critical point between the phases. By doubling the unit cell in two directions, we discuss spin-1/2 HAF on a square lattice using the suggested four-spin BOT. We identify the magnon and the amplitude (Higgs) modes among fifteen spin-2, spin-1, and spin-0 quasiparticles arising in the theory. The magnon spectrum,
E, and
M found in the first order in
1/n are in good quantitative agreement with previous numerical and experimental results. We observe a special moderately damped spin-0 quasiparticle (``singlon'' for short) whose energy is smaller than the energy of the Higgs mode in the most part of the Brillouin zone. By considering HAF with Ising-type anisotropy, we find that both Higgs and singlon modes stem from two-magnon bound states, which merge with two-magnon continuum not far from the isotropic limit. We demonstrate that singlons appear explicitly in ``scalar'' correlators one of which describes the Raman intensity in
B1g symmetry. The latter is expressed in the leading order in
1/n via the singlon Green's function at zero momentum, which shows an asymmetric peak. The position of this peak given by the singlon energy coincides with the position of the so-called ``two-magnon'' peak observed experimentally in, e.g., layered cuprates.
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) and at the magnetic ordering wavevectors
±[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.
Investigation of dynamical excitations is difficult but crucial to the understanding of many exotic quantum phenomena discovered in quantum materials. This is particularly true for highly frustrated quantum antiferromagnets whose dynamical properties deviate strongly from theoretical predictions made based on the spin-wave or other approximations. Here, we present a large-scale numerical calculation on the dynamical correlation functions of spin-1/2 triangular Heisenberg model using a state-of-the-art tensor network renormalization group method. The calculated results allow us to gain for the first time a comprehensive picture on the nature of spin excitation spectra in this highly frustrated quantum system. It provides a quantitative account for all the key features of the dynamical spectra disclosed by inelastic neutron scattering measurements for Ba_{3}CoSb_{2}O_{9}, revealing the importance of the interplay between low- and high-energy excitations and its renormalization effect to the low-energy magnon bands and high-energy continuums. We identify the longitudinal Higgs modes in the intermediate-energy scale and predict the energy and momentum dependence of spectral functions along the three principal axes that can be verified by polarized neutron scattering experiments. Furthermore, we find that the spin excitation spectra weakly depend on the anisotropic ratio of the antiferromagnetic interaction.
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.