The transverse component of the dynamic form factor (\mathscr{S}^{x}(k, \omega )) of the Ising-like linear chain at various temperatures is studied by the perturbation theory about the transverse part of the Hamiltonian. The dynamic form factor (\mathscr{S}^{x}(k, \omega )) for both the ferromagnetic and antiferromagnetic couplings has the three-peak structure for k =0 at finite temperatures, and this structure persists even for any wave vector k and at any high temperature. Many interesting characters in (\mathscr{S}^{x}(k, \omega )) are obtained. The k -dependence of width of the absorption peak is remarkable in the antiferromagnetic case. The absorption peak has a finite width even at absolute zero except for k = π/2 in the antiferromagnetic case, while the shape of the absorption peak is reduced to a infinitely sharp one as the temperature is decreased to absolute zero in the ferromagnetic case.
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.
The spin dynamics of an Ising-like S =1/2 antiferromagnet with a weak next-nearest-neighbor interaction on a linear chain is studied by a perturbation method. Bound states of two domain walls, i.e., 2-soliton bound states, are found in addition to soliton-pair states. When the next-nearest-neighbor interaction is ferromagnetic, the dynamical structure factor S x x ( k , ω) exhibits a sharp peak at a lower energy and a tail at higher energies. Our results are in good agreement with experimental observations of S x x ( k , ω) on CsCoCl 3 and CsCoBr 3 at low temperatures.
The dynamic structure factor of the spin-
21 transverse Ising chain is obtained by means of a numerical approach suggested earlier [O. Derzhko and T. Krokhmalskii, Ferroelectrics 192, 21 (1997)]. Frequency shapes of the dynamic structure factor at various values of the wave vector, transverse field, and temperature are displayed and discussed.
We present results for the dynamic structure factor of the
S=1∕2 bond alternating Heisenberg chain over a large range of frequencies and temperatures. Data are obtained from a numerical evaluation of thermal averages based on the calculation of all eigenvalues and eigenfunctions for chains of up to 20 spins. Interpretation is guided by the exact temperature dependence in the noninteracting dimer limit which remains qualitatively valid up to an interdimer exchange $\ensuremath{\lambda}\ensuremath{\approx}0.5$. The temperature induced central peak around zero frequency is clearly identified and aspects of the crossover to spin diffusion in its variation from low to high temperatures are discussed. The one-magnon peak acquires an asymmetric shape with increasing temperature. The two-magnon peak is dominated by the
S=1 bound state which remains well defined up to temperatures of the order of
J. The variation with temperature and wave vector of the integrated intensity for one-magnon and two-magnon scattering and of the central peak are discussed.
Results are presented and interpreted for the zero- and finite-temperature excitation spectrum of ferromagnetic Ising-Heisenberg chains, as probed by dynamic form factors. Finite-chain calculations demonstrate the occurrence of a thermally induced resonance centered around zero frequency, and a broadening of the magnon and two-magnon bound-state resonances at low
T. The occurrence of bound states in the associated transitions demonstrates the failure of finite-order magnon perturbation theory.
The dynamics of quantum solitons in an Ising-like S=(1/2 antiferromagnet on finite linear chains with spins N (\ensuremath{\le}15) is studied by integrating the Schr\"odinger equation of motion. Space-time correlation functions
Szz(r,t) and their Fourier transforms, i.e., dynamical structure factor
Szz(q,\ensuremath{\omega}), are calculated for both even and odd N. A slow but large oscillation of
Szz(r,t) is seen, which gives a direct evidence of the occurrence of propagating domain walls, i.e., solitons. The oscillation leads to a low-energy component of
Szz(q,\ensuremath{\omega}) whose line shape greatly depends on whether N is even or odd and on the temperature. We analyze in detail the dependence of soliton number in the line shape and give a plausible conjecture that
Szz(q,\ensuremath{\omega}) for N=\ensuremath{\infty} should exhibit a very broad double maximum at low temperatures. We estimate
Szz(q,\ensuremath{\omega}) at various temperatures. Our results reproduce experimental observations of
Szz(q,\ensuremath{\omega}) on
CsCoCl3 and
CsCoBr3 very well over a wide temperature range.