The influence of the nonlinearity of the spin equations of motion on the dynamic structure factor of the antiferromagnetic Heisenberg chain in an external field is calculated in the low-temperature limit. The memory functions for the longitudinal and transverse spin component are calculated rigorously to lowest nonvanishing order in the temperature. In this limit, only two-magnon processes contribute to the memory functions. Divergencies in the two-magnon density of states give rise to resonances in addition to the usual spin-wave peak in the dynamic structure factor.
The magnetic-field effect on the transverse and longitudinal spin fluctuation spectra is studied for one-dimensional spin 1/2 isotropic Heisenberg antiferromagnet. We perform an exact calculation of dynamical correlation functions for finite-spin chains. The result shows that a large portion of the intensity is concentrated on the des Cloizeaux-Pearson spectrum, which was studied previously for finite-magnetic-field case by the authors (Prog. Theor. Phys. 57 (1977), 1862). This observation is combined with general considerations on dynamical correlation functions. We compare the present theory with Heilmann et al.'s neutron experiment on CuCl2·2NC5D5. A study is made also on the magnetic-field dependence of the static correlation functions. The longitudinal static correlation function in particular shows interesting wave-vector dependence, which is worth investigating experimentally.
We present a study of the dynamic structure factor of the antiferromagnetic spin-
21 Heisenberg chain at finite temperatures and finite magnetic fields. Using quantum Monte Carlo based on the stochastic series expansion and maximum entropy methods, we evaluate the longitudinal and the transverse dynamic structure factors from vanishing magnetic fields up to and above the threshold
Bc for ferromagnetic saturation, as well as for high and for intermediate temperatures. We study the field-induced redistribution of spectral weight contrasting longitudinal versus transverse excitations. At finite fields below saturation incommensurate low-energy modes are found consistent with zero-temperature Bethe ansatz. The crossover between the field-induced ferromagnet above
Bc and the Luttinger liquid below
Bc is analyzed in terms of the transverse spin dynamics. Evaluating sum rules we assess the quality of the analytic continuation and demonstrate excellent consistency of the maximum entropy results.
Spin-dynamical calculations on one-dimensional systems have relied heavily on classical ($s=\ensuremath{\infty}$) theories, despite abundant evidence that quantum effects can be extremely important at low temperatures. We present a new approach to the spin dynamics of the one-dimensional isotropic
s=21 Heisenberg antiferromagnetic (HB AF) which does not involve the many-body techniques usually employed. It is based on analytic Bethe ansatz calculations of excitation energies and densities of states combined with finite-chain calculations of matrix elements. An important feature of our method is the use of rigorous selection rules and the introduction of new selection rules, which are valid for macroscopic systems in a magnetic field. We show that in zero field the dynamical two-spin correlation function ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at
T=0 is governed by a two-parameter continuum of spin-wave-type excitations. In nonzero field, the longitudinal component ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ and the transverse components ${S}_{\mathrm{xx}}(q,\ensuremath{\omega})\ensuremath{\equiv}{S}_{\mathrm{yy}}(q,\ensuremath{\omega})$ behave quite differently because they are dominated by different continua of excitations. The former is characterized by a lowest excitation branch with a zero-frequency mode moving from the zone boundary ($q=\ensuremath{\pi}$) towards the zone center (
q=0) as the field increases, whereas the latter is characterized by a lowest branch with a zero frequency mode moving from $q=0 \mathrm{to} \ensuremath{\pi}$ with increasing field. The first part of our work features an approximate analytic expression for ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ at zero temperature and in zero field. Although our expression is not rigorous, exact sum rules are violated only by a small amount, and good agreement exists with the few known exact results. Our studies are extended to nonzero temperatures by placing major reliance on exact finite-chain calculations. Our work was stimulated by recent neutron scattering experiments and is oriented towards experimental comparisons. Our result for the
s=21 integrated intensity is in much better agreement with neutron scattering data on Cu
Cl2\ifmmode\cdot\else\textperiodcentered\fi{}2N(
C5D5) (CPC) than the corresponding semiclassical result. Moreover, the spectral-weight distribution in ${S}_{\ensuremath{\mu}\ensuremath{\mu}}(q,\ensuremath{\omega})$ shows increasing asymmetry as $q\ensuremath{\rightarrow}\ensuremath{\pi}$, a quantum effect, again in agreement with more recent neutron scattering data. The second part of our work deals with the effects of an applied magnetic field. We extend the analytic work of Ishimura and Shiba to obtain expressions for the energies and densities of states of the various excitation continua. It is shown that these continua are expected to give rise to multiple structures in the scattering intensity. Our results appear to be in quantitative agreement with preliminary results of a neutron study in CPC in a field of 70 kOe, revealing anomalous scattering intensity peaks. Our results repeatedly demonstrate the inadequacy of classical spin-wave theory for this problem. They call for additional experimental studies on quasi-one-dimensional antiferromagnets to examine other unusual and interesting phenomena predicted by our approach.
The dynamic structure factor of the energy density fluctuations in the classical Heisenberg chain is studied theoretically. Using exact expressions for the first six frequency moments and the knowledge of the exact
T=0 result, simple approximations are used to calculate the spectrum. We show rigorously that the time-dependent correlation function is different for ferro-and antiferromagnetic coupling if $T\ensuremath{\ne}0$.