Magnetic-field tuning of equal-time longitudinal and transverse correlations is investigated for the antiferromagnetic isotropic spin-1/2 Heisenberg chain. Full exact diagonalization of a ten-site periodic ring is used at kBT/J=0.15 over 0≤h/J≤2.6, where h=gμBB. The field breaks spin-rotational symmetry, increases uniform magnetization, redistributes longitudinal and transverse correlation weight, and drives the system toward the fully polarized state above the saturation field hs=2J. Below saturation, longitudinal correlations acquire a uniform m² background and field-dependent oscillatory structure, whereas transverse antiferromagnetic correlations weaken as the density of reversed spins decreases. The finite-temperature magnetization rounds the zero-temperature level crossings and saturation threshold. The numerical results are interpreted using the Tomonaga-Luttinger-liquid description and checked against exact limiting values. The analysis provides a reproducible finite-chain account of field-controlled spin correlations and identifies the distinctions required when connecting static calculations to scattering experiments.
The thermal evolution of equal-time spin correlations in the antiferromagnetic isotropic spin-1/2 Heisenberg chain is examined by full exact diagonalization of a ten-site periodic cluster. The calculation retains the complete spectrum and evaluates canonical ensemble averages without decoupling approximations. Correlations through the maximum independent separation are reported over 0.10 ≤ kBT/J ≤ 5. The low-temperature state displays the expected alternating antiferromagnetic pattern and appreciable correlations across the finite ring. Heating suppresses the magnitude of every nonlocal correlator, with longer-range terms disappearing first. The nearest-neighbour correlation approaches the high-temperature limit continuously, while an effective finite-cluster correlation length falls rapidly around kBT/J of order unity. Low- and high-temperature consistency checks, SU (2) symmetry, and comparison with Bethe-ansatz expectations are used to validate the computation. The results provide a compact reproducible reference for interpreting thermal loss of short-range order, while clearly separating finite-size numerical evidence from thermodynamic-limit conclusions.
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.
Inelastic neutron scattering is employed to study transverse spin correlations of a Heisenberg
S=1/2 chain compound in a magnetic field of 7.5 T. The target compound is the antiferromagnetic Heisenberg
S=1/2 chain material 2(1,4-dioxane)$\ifmmode\cdot\else\textperiodcentered\fi{}2({\mathrm{H}}_{2}\mathrm{O})\ifmmode\cdot\else\textperiodcentered\fi{}{\mathrm{CuCl}}_{2}$, or CuDCl for short. The validity and the limitations of the scaling relation for the transverse dynamic structure factor are tested, discussed, and compared to the Tomonaga-Luttinger spin liquid theory and to Bethe-ansatz results for the Heisenberg model.
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.
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.