Spinons, Solitons and Magnons in One-dimensional Heisenberg-Ising Antiferromagnets

We calculate the excitation spectra for the one-$d$ Heisenberg-Ising antiferromagnets by expansions around the Ising limit. For $S=1/2$, the calculated expansion coefficients for the spinon-spectra agree term by term with the solution of Johnson and McCoy. For $S=1$, the solitons become gapless before the Heisenberg limit is reached, signalling a transition to the Haldane phase. By applying a staggered field we calculate the one-magnon spectra for the $S=1$ Heisenberg chain. For $S=3/2$ the quantum renormalization of the spin-wave spectra is calculated to be approximately $1.16$.Comment: 4 pages, RevTex, 3 postscript figures, Latex file and figures have been uuencode

Large-Scale Numerical Evidence for Bose Condensation in the S=1 Antiferromagnetic Chain in a Strong Field

Using the recently proposed density matrix renormalization group technique we show that the magnons in the S=1 antiferromagnetic Heisenberg chain effectively behaves as bosons that condense at a critical field h_c.Comment: 12 pages, REVTEX 3.0, 3 postscript figures appended, UBCTP-93-00

S(k) for Haldane Gap Antiferromagnets: Large-scale Numerical Results vs. Field Theory and Experiment

The structure function, S(k), for the s=1, Haldane gap antiferromagnetic chain, is measured accurately using the recent density matrix renormalization group method, with chain-length 100. Excellent agreement with the nonlinear $\sigma$ model prediction is obtained, both at $k\approx \pi$ where a single magnon process dominates and at $k\approx 0$ where a two magnon process dominates. We repeat our calculation with crystal field anisotropy chosen to model NENP, obtaining good agreement with both field theory predictions and recent experiments. Correlation lengths, gaps and velocities are determined for both polarizations.Comment: 11 pages, 3 postscript figures included, REVTEX 3.0, UBCTP-93-02

Equal Time Correlations in Haldane Gap Antiferromagnets

The $S=1$ antiferromagnetic Heisenberg chain both with and without single ion anisotropy is studied. Using the recently proposed density matrix renormalization group technique we calculate the energy gaps as well as several different correlation functions. The two gaps, $\Delta_{||}, \Delta_\perp$, along with associated correlation lengths and velocities are determined. The numerical results are shown to be in good agreement with theoretical predictions derived from the nonlinear sigma model and a free boson model. We also study the $S=1/2$ excitations that occur at the ends of open chains; in particular we study the behavior associated with open boundary conditions, using a model of $S=1/2$ spins coupled to the free bosons.Comment: 32 pages, uufiles encoded REVTEX 3.0, 19 postscript figures included, UBCTP-93-02

Properties of Haldane excitations and multiparticle states in the antiferromagnetic spin-1 chain compound CsNiCl₃

We report inelastic time-of-flight and triple-axis neutron scattering measurements of the excitation spectrum of the coupled antiferromagnetic spin-1 Heisenberg chain system CsNiCl3. Measurements over a wide range of wave-vector transfers along the chain confirm that above T_N CsNiCl3 is in a quantum-disordered phase with an energy gap in the excitation spectrum. The spin correlations fall off exponentially with increasing distance with a correlation length xi=4.0(2) sites at T=6.2K. This is shorter than the correlation length for an antiferromagnetic spin-1 Heisenberg chain at this temperature, suggesting that the correlations perpendicular to the chain direction and associated with the interchain coupling lower the single-chain correlation length. A multi-particle continuum is observed in the quantum-disordered phase in the region in reciprocal space where antiferromagnetic fluctuations are strongest, extending in energy up to twice the maximum of the dispersion of the well-defined triplet excitations. We show that the continuum satisfies the Hohenberg-Brinkman sum rule. The dependence of the multi-particle continuum on the chain wave-vector resembles that of the two-spinon continuum in antiferromagnetic spin-1/2 Heisenberg chains. This suggests the presence of spin-1/2 degrees of freedom in CsNiCl3 for T < 12K, possibly caused by multiply-frustrated interchain interactions.Comment: 15 pages revtex, submitted to PR