Critical exponents for alternation in Heisenberg antiferromagnetic chains

The ground-state energy per site, λ(δ), and singlet-triplet gap, ΔE(δ), of regular (δ=0) and alternating (δ ≤ 0.01) Heisenberg antiferromagnetic chains are obtained by extrapolating exact numerical solutions of even and odd rings and chains of N ≤ 20 spins. The critical exponents of 1.72 ± 0.02 for λ(δ) and 0.9 ± 0.1 for ΔE(δ) are compared with recent theoretical results for spin-Peierls transitions. Interactions among spinless fermions alter the instability to alternation.     

System-size effect versus staggered magnetization in the antiferromagnetic Heisenberg XXZ chains: A Monte Carlo study

Monte Carlo simulations of the antiferromagnetic Heisenberg XXZ chains are carried out on a larger system than in a previous paper. System-size effect versus staggered magnetization is severe in the vicinity of the anisotropy parameter Δ = 1.0. The result obtained for spin-1 supports Haldane's conjecture that a gap exists in the excitation spectrum in the vicinity of Δ = 1.0.     

Quantized spin waves in antiferromagnetic Heisenberg chains

The quantized stationary spin wave modes in one-dimensional antiferromagnetic spin chains with easy axis on-site anisotropy have been studied by means of Landau-Lifshitz-Gilbert spin dynamics. We demonstrate that the confined antiferromagnetic chains show a unique behavior having no equivalent, neither in ferromagnetism nor in acoustics. The discrete energy dispersion is split into two interpenetrating n and n' levels caused by the existence of two sublattices. The oscillations of individual sublattices as well as the standing wave pattern strongly depend on the boundary conditions. Particularly, acoustical and optical antiferromagnetic spin waves in chains with boundaries fixed (pinned) on different sublattices can be found, while an asymmetry of oscillations appears if the two pinned ends belong to the same sublattice.     

Exchange narrowing in random-exchange Heisenberg antiferromagnetic chains

A phenomenological theory of exchange narrowing is developed for random-exchange Heisenberg antiferromagnetic chains at low temperature. The nearly logarithmic epr linewidth of quinolinium (tetracyanoquino-dimethane)₂ is regained as an inhomogeneous superposition of thermally decoupled domains with widely different renormalized exchange fields that also describe the static thermodynamics. The temperature dependence of internal dipolar fields and of interchain interactions are modeled in terms of spin dilution.     

Nonlocal topological order in antiferromagnetic Heisenberg chains

We demonstrate the existence of nonlocal topological (string) order in half-integer-spin antiferromagnetic Heisenberg chains on macroscopic scale on the basis of analytical scaling analysis and density matrix renormalization group calculations. Strong numerical evidence leads to a conjecture that chains with S = (2m-1)/2 and m (m = integers) belong to the same topological class defined by the topological angle theta/pi = 1/m that plays a role similar to the fictitious gauge field in the fractional quantum Hall effect.     

String order in half-integer-spin antiferromagnetic Heisenberg chains

We derive the extended string order parameter O(S) for antiferromagnetic Heisenberg chains with half-integer spin S in the valence-bond-solid picture. We obtain the analytic power-law scaling of O(S) versus the chain length L and show that O(S) scales at an extremely slow pace that decreases rapidly with growing spin magnitude. Furthermore, accurate numerical calculations show that the power-law scaling sets in only when L exceeds a characteristic length scale l(S) which increases very fast with growing S. Consequently, a pseudo-long-range string order exists in half-integer-spin Heisenberg chains. The implications of this result and its relationship to other topological features such as the end-chain states are discussed.     

Field dependent spin dynamics of antiferromagnetic Heisenberg chains

Low temperature data are given for the spectra of longitudinal and transverse correlation functions of an antiferromagnetic classical heisenberg chain. The one dimensional magnet subjected to large external fields is investigated by means of a computer simulation calculation. The results are tied in with the static properties and compared with theoretical predictions.     

Dynamic magnetization reversal and bistable states in antiferromagnetic multilayer structures

The dynamic behavior of the magnetization under a transverse microwave field is investigated in a system of magnetic layers with cubic crystallographic anisotropy coupled through interlayer antiferromagnetic exchange interaction. An orientational phase transition is found to occur as the microwave field frequency and amplitude are varied. It is established that there is a frequency range in which several steady-state regimes of precession of magnetic moments exist. The limits of this range can be efficiently controlled both by varying the strength of the bias magnetic field and the amplitude of the microwave field.     

Dynamics of antiferromagnetic Ising model with fixed magnetization

The dynamical critical exponent z of the Ising antiferromagnet under the constraint of a fixed zero magnetization is verified by Monte Carlo simulations to be compatible with that of the usual Glauber dynamics of model A, while for positive magnetization the exponent seems different. We also determine the diffusivity of the magnetization and finite size effects. Received: 18 June 1997 / Revised: 28 July 1997 / Accepted: 13 October 1997     

The valence-bond representation of the three dimensional antiferromagnetic Heisenberg model

We present results on the specific heat and the staggered magnetization of the three dimensional antiferromagnetic Heisenberg model. These results are obtained from a numerical solution of the approximated evolution equation for the expectation values of the Boltzmann factor between valence-bond states.