We discuss a spin-
21 Heisenberg antiferromagnet on the triangular lattice using the recently proposed bond-operator technique (BOT). We use the variant of the BOT which takes into account all spin degrees of freedom in the magnetic unit cell containing three spins. Apart from conventional magnons known from the spin-wave theory (SWT), there are high-energy collective excitations in the BOT which are built from high-energy excitations of the magnetic unit cell. We also obtain another high-energy quasiparticle which has no counterpart not only in the SWT but also in the harmonic approximation of the BOT. All observed elementary excitations produce visible anomalies in dynamical spin correlators. We show that quantum fluctuations considerably change properties of conventional magnons predicted by the SWT. The effect of a small easy-plane anisotropy is discussed. The anomalous spin dynamics with multiple peaks in the dynamical structure factor is explained that was observed recently experimentally in
Ba3CoSb2O9 and which the SWT could not describe even qualitatively.
We study the field dependence of the antiferromagnetic spin-
21 Heisenberg model on the square lattice by means of exact diagonalizations. In the first part, we calculate the spin-wave velocity
c, the spin stiffness ${\ensuremath{\rho}}_{s}$, and the magnetic susceptibility ${\ensuremath{\chi}}_{\ensuremath{\perp}}$, and thus determine the microscopic parameters of the low-energy long-wavelength description. In the second part, we present a comprehensive study of dynamical spin-correlation functions for magnetic fields ranging from zero up to saturation. We find that, at low fields, magnons are well defined in the whole Brillouin zone but the dispersion is substantially modified by quantum fluctuations compared to the classical spectrum. At higher fields, decay channels open and magnons become unstable with respect to multimagnon scattering. Our results directly apply to inelastic neutron-scattering experiments.
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.
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.
The nearest-neighbor quantum antiferromagnetic (AF) Heisenberg model for spin-
1∕2 on a two-dimensional square lattice is studied in the auxiliary-fermion representation. Expressing spin operators by canonical fermionic particles requires a constraint on the fermion charge
Qi=1 on each lattice site
i, which is imposed approximately through the thermal average. The resulting interacting fermion system is first treated in mean-field theory (MFT), which yields an AF ordered ground state and spin waves in quantitative agreement with conventional spin-wave theory. At finite temperature a self-consistent approximation beyond mean field is required in order to fulfill the Mermin-Wagner theorem. We first discuss a fully self-consistent approximation, where fermions are renormalized due to fluctuations of their spin density, in close analogy to FLEX. While static properties like the correlation length, $\ensuremath{\xi}(T)\ensuremath{\propto}\mathrm{exp}(aJ∕T)$, come out correctly, the dynamical response lacks the magnon-like peaks which would reflect the appearance of short-range order at low
T. This drawback, which is caused by overdamping, is overcome in a ``minimal self-consistent approximation'' (MSCA), which we derive from the equations of motion. The MSCA features dynamical scaling at small energy and temperature and is qualitatively correct both in the regime of order-parameter relaxation at long wavelengths $\ensuremath{\lambda}>\ensuremath{\xi}$ and in the short-range-order regime at $\ensuremath{\lambda}<\ensuremath{\xi}$. We also discuss the impact of vertex corrections and the problem of pseudo-gap formation in the single-particle density of states due to long-range fluctuations. Finally we show that the (short-range) magnetic order in MFT and MSCA helps to fulfill the constraint on the local fermion occupancy.
A key feature of the newly discovered altermagnet is that its spin degeneracy is lifted, although it has an antiferromagnetic order and zero net magnetization. In this work, we investigate a frustrated spin-1/2
J1-
J2-
δ Heisenberg model on the square lattice by the tensor network methodin combination with the linear spin-wave theory, with our focus on both the magnon excitations and longitudinal excitations.For a small
J2 and a finite range of
δ we demonstrate that such a model hosts an altermagnetic ground state. Its magnon spectrum is split into two branches and the largest splitting occurs at
(±π/2,±π/2) in the Brillouin zone. The magnitudes of splitting in the two magnon modes are equal with respect to the case of
δ=0. Dynamical spin structure factors show that the low-energy peak in the longitudinal spectral weight around
(π/2,π/2) is also split, and thus the relative positions of the magnon modes and longitudinal modes in energy may change in the presence of a finite
δ. These findings demonstrate that the altermagnets harbor more complex quantum dynamics than the conventional collinear antiferromagnets.