Dynamics of one-dimensional Ising-like (strongly anisotropic) antiferromagnets is studied by the perturbation theory from the pure Ising limit and by an exact calculation for finite chains. Both calculations show that the des Cloizeaux-Gaudin (dC-G) “spin-wave” spectrum corresponds neither to a lower bound of excitation continuum nor to the peak position of the transverse response Sxx(Q, ω). A new interpretation is given of the spin-wave spectrum of CsCoCl3 without relying on the dC-G theory. It is also shown that at elevated temperatures Sxx(Q, ω) has a three-peak structure. The longitudinal response Sxx(Q, ω) at low temperatures has a weak peak at the position of spin wave peak, while with increasing temperature Sxx(Q, ω) is dominated by the central peak due to thermally activated solitons, which was predicted by Villain.
Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.
We consider the one-dimensional Ising-like fully anisotropic S = 1/2 Heisenberg antiferromagnetic Hamiltonian and study the dynamics of domain wall excitations in the presence of a transverse magnetic field h x . We obtain dynamical spin correlation functions along the magnetic field, S xx ( q ,ω), and perpendicular to it, S yy ( q ,ω). It is shown that the line shapes of S xx ( q ,ω) and S yy ( q ,ω) are purely symmetric at the zone boundary. It is observed in S yy ( q ,ω) for π/2< q <π that the spectral weight moves toward the low-energy side with the increase of h x . This model is applicable to the study of the spin dynamics of CsCoCl 3 in the presence of weak interchain interactions.
The anisotropic
XXZ spin-
21 Heisenberg chain is studied using renormalization-group theory. The specific heats and nearest-neighbor spin-spin correlations are calculated throughout the entire temperature and anisotropy ranges in both ferromagnetic and antiferromagnetic regions, obtaining a global description and quantitative results. We obtain, for all anisotropies, the antiferromagnetic spin-liquid spin-wave velocity and the Ising-like ferromagnetic excitation spectrum gap, exhibiting the spin-wave to spinon crossover. A number of characteristics of purely quantum nature are found: The in-plane interaction
sixsjx+siysjy induces an antiferromagnetic correlation in the out-of-plane
siz component, at higher temperatures in the antiferromagnetic
XXZ chain, dominantly at low temperatures in the ferromagnetic
XXZ chain, and, in-between, at all temperatures in the
XY chain. We find that the converse effect also occurs in the antiferromagnetic
XXZ chain: an antiferromagnetic
sizsjz interaction induces a correlation in the
sixy component. As another purely quantum effect, (i) in the antiferromagnet, the value of the specific heat peak is insensitive to anisotropy and the temperature of the specific heat peak decreases from the isotropic (Heisenberg) with introduction of either type (Ising or
XY) of anisotropy; and (ii) in complete contrast, in the ferromagnet, the value and temperature of the specific heat peak increase with either type of anisotropy.
The one-dimensional Heisenberg antiferromagnet with 8=1/2 is treated with the use of the Fermi operators and an additional condition that the long-range order is absent.Our spin wave spectrum of a one-dimensional Heisenberg antiferromagnet without longrange order is expressed by andThis is in good agreement with the exact spin wave spectrum role =1!'/2lsin kl which is obtained by des Cloizeaux and Pearson at T=O.Correlation functions <S1S2> and <SlSs> are in good agreement with the exact value at T=O, also.Thermodynamic properties of this system agree with those of Bulaevskii and those of Katsura and Inawashiro. § I. IntroductionThe one-dimensional Heisenberg antiferromagnet has been investigated by many authors.Most of previous theories have been for either zero or infinite temperatures.Recently various experiment on (CD3) 4NMnCl 3 (TMMC)ll requires further theoretical work of a Heisenberg linear-chain magnet for finite temperatures.The experimental results of linear antiferromagnet show that at low temperatures there are long-lived spin waves in spite of the absence of long-range order.At T= 0, the spin wave spectrum, wqoc I sin ql, is gained approximately by Anderson 2 l and exactly by des Cloizeaux and Pearson.8 l Recently Richards, 4 l Scales and Gersh, 5 l Kondo and Yamaji 6 l obtained the spin wave spectrum of linear antiferromagnet at finite temperatures with the use of the second-order Green's function theory.The spin wave spectrum, however, does not show exactly wqoc I sin ql at finite temperatures.
Recent low-temperature inelastic neutron scattering data on the quasi-one-dimensional (1D) Heisenberg-Ising antiferromagnet (AFM) CsCo
Cl3 call for new theoretical efforts, for the available theories fail to explain the observed line shapes. In this paper we initiate a detailed study of the dynamical properties of the 1D spin-\textonehalf{} anisotropic
XYZ AFM with emphasis on the dynamic structure factor ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at
T=0. The structure of ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ is determined by the combined effects of the density of states and the matrix elements. Both effects are discussed for selected cases: the
XY-Heisenberg AFM (planar system), the Heisenberg-Ising AFM (uniaxial system), and the
XY-Ising AFM (biaxial system). The exact solution for ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ of the
XY-Ising AFM has already many features in common with the experimental data on CsCo
Cl3. It is an ideal starting point for a perturbation approach to the Heisenberg-Ising AFM.