We present an approximate analytic expression for the dynamical spin correlation function of the S=1/2 linear Heisenberg antiferromagnet at T=0. The basis for our approach is that in zero field the spectrum is dominated by a double continuum [in (q,ω) -space] of triplet spin wave excitations. The S=1/2 integrated intensity agrees very well with recent neutron scattering results on CPC, unlike the corresponding classical intensity. Moreover, the S=1/2 spectral weight function shows increasing asymmetry as q→π, a quantum effect, observable in more recent neutron scattering data. In non-zero magnetic field, there exist two, partly overlapping, double continua, each giving rise to a peak situated at the lower boundary. The (zz component of) spectral weight function therefore has a double-peaked structure, as observed experimentally. Theory and experiment are in apparent agreement concerning the energy difference between the peaks.
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 author calculates the dynamical structure factors of a two-dimensional Heisenberg antiferromagnet at T=0, to order 1/(2S) 2 , taking careful account of the umklapp processes. It is shown that, for the transverse spin part, the terms of order 1/(2S) 2 give rise to a broad sideband peak of three-magnon excitations, whose intensity is small but not negligible. For the longitudinal spin part, the terms of order 1/(2S) 2 modify noticeably the spectral shape of the continuum of two-magnon excitations as a function of frequency. These results could be observed in future neutron scattering experiments.
The spin fluctuations parallel to the external magnetic field in the ground state of the one-dimensional (1D)
s=21 Heisenberg antiferromagnet are dominated by a two-parameter set of collective excitations. In a cyclic chain of N sites and magnetization
0<Mz<N/2, the ground state, which contains
2Mz spinons, is reconfigured as the physical vacuum for a different species of quasiparticles, identifiable in the framework of the coordinate Bethe ansatz by characteristic configurations of Bethe quantum numbers. The dynamically dominant excitations are found to be scattering states of two such quasiparticles. For $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty},$ these collective excitations form a continuum in $(q,\ensuremath{\omega})$ space with an incommensurate soft mode. Their matrix elements in the dynamic spin structure factor ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ are calculated directly from the Bethe wave functions for finite N. The resulting line- shape predictions for $\stackrel{\ensuremath{\rightarrow}}{N}\ensuremath{\infty}$ complement the exact results previously derived via algebraic analysis for the exact two-spinon part of ${S}_{\mathrm{zz}}(q,\ensuremath{\omega})$ in the zero-field limit. They are relevant for neutron-scattering experiments on quasi-1D antiferromagnetic compounds in a strong magnetic field.
The exact expression derived by Bougourzi, Couture, and Kacir for the two-spinon contribution to the dynamic spin structure factor S(q,\ensuremath{\omega}) of the one-dimensional s=1/2 Heisenberg antiferromagnet at T=0 is evaluated for direct comparison with finite-chain transition rates (N\ensuremath{\leqslant}28) and an approximate analytical result previously inferred from finite-N data, sum rules, and Bethe ansatz calculations. The two-spinon excitations account for 72.89% of the total intensity in S(q,\ensuremath{\omega}). The singularity structure of the exact result is determined analytically and its spectral-weight distribution evaluated numerically over the entire range of the two-spinon continuum. The leading singularities of the frequency-dependent spin autocorrelation function, static spin structure factor, and q dependent susceptibility are determined via sum rules. The impact of the non-two-spinon excitations on the integrated intensity, the susceptibility, the frequency moments, and the Euclidian time representation of S(q,\ensuremath{\omega}) is studied on the basis of finite-size data.
We investigate the spin dynamics of the square-lattice spin- 1/2 Heisenberg antiferromagnet by means of an improved mean-field Schwinger boson calculation. By identifying both, the long-range Neel and the RVB-like components of the ground state, we propose an educated guess for the mean-field magnetic excitation consisting on a linear combination of local and bond spin flips to compute the dynamical structure factor. Our main result is that when this magnetic excitation is optimized in such a way that the corresponding sum rule is fulfilled, we recover the low- and high-energy spectral weight features of the experimental spectrum. In particular, the anomalous spectral weight depletion at (π, 0) found in recent inelastic neutron scattering experiments can be attributed to the interference of the triplet bond excitations of the RVB component of the ground state. We conclude that the Schwinger boson theory seems to be a good candidate to adequately interpret the dynamic properties of the square-lattice Heisenberg antiferromagnet.