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.     

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.     

Effects of two energy scales in weakly dimerized antiferromagnetic quantum spin chains

By means of thermal expansion and specific heat measurements on the high-pressure phase of (VO)(2)P(2)O(7), the effects of two energy scales of the weakly dimerized antiferromagnetic S=1/2 Heisenberg chain are explored. The low-energy scale, given by the spin gap Delta, is found to manifest itself in a pronounced thermal expansion anomaly. A quantitative analysis, employing the density-matrix renormalization-group approach for transfer matrices calculations, shows that this feature originates from changes in the magnetic entropy with respect to Delta, partial differentialS(m)/partial differentialDelta. This term, inaccessible by specific heat, is visible only in the weak-dimerization limit, where it reflects peculiarities of the excitation spectrum and its sensitivity to variations in Delta.     

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.     

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.     

Excitations in a four-leg antiferromagnetic Heisenberg spin tube

Inelastic neutron scattering is used to investigate magnetic excitations in the quasi-one-dimensional quantum spin-liquid system Cu(2)Cl(4).D(8)C(4)SO(2). Contrary to previously conjectured models that relied on bond-alternating nearest-neighbor interactions in the spin chains, the dominant interactions are actually next-nearest-neighbor in-chain antiferromagnetic couplings. The appropriate Heisenberg Hamiltonian is equivalent to that of a S=1/2 4-leg spin-tube with almost perfect one dimensionality and no bond alternation. A partial geometric frustration of rung interactions induces a small incommensurability of short-range spin correlations.     

Thermodynamics of antiferromagnetic alternating spin chains

We consider integrable quantum spin chains with alternating spins (S₁,S₂)$(S_1,S_2)$. We derive a finite set of non-linear integral equations for the thermodynamics of these models by use of the quantum transfer matrix approach. Numerical solutions of the integral equations are provided for quantities like specific heat, magnetic susceptibility and in the case S₁=S₂$S_1=S_2$ for the thermal Drude weight. At low temperatures one class of models shows finite magnetization and the other class presents antiferromagnetic behaviour. The thermal Drude weight behaves linearly on T at low temperatures and is proportional to the central charge c   of the system. Quite generally, we observe residual entropy for S₁≠S₂$S_1\ne S_2$.     

Frustrated antiferromagnetic spin 1 Heisenberg model with single ion anisotropy on a simple cubic lattice

We study the effects of frustration between nearest, next-nearest neighbor and next-next-nearest neighbors (NNN) of the quantum S=1 anisotropic antiferromagnetic Heisenberg model on a simple cubic lattice with single ion anisotropy using the bond operator technique. We calculate the phase diagram at zero temperature and the gap as a function of temperature in the disordered paramagnetic phase.     

Coupled quantum spin chains: how does the gap depend on the interchain interaction?

In this note we show that a naive use of the mean field approximation to treat the interchain interaction in a quasi-one dimensional ferromagnet may lead to a spurious gap.     

Haldane-like antiferromagnetic spin chain in the large anisotropy limit

We consider the one dimensional, periodic spin chain with N sites, similar to the one studied by Haldane [1], however in the opposite limit of very large anisotropy and small nearest neighbour, anti-ferromagnetic exchange coupling between the spins, which are of large magnitude s. For a chain with an even number of sites we show that actually the ground state is non-degenerate and given by a superposition of the two Neél states, due to quantum spin tunnelling. With an odd number of sites, the Neél state must necessarily contain a soliton. The position of the soliton is arbitrary thus the ground state is N-fold degenerate. This set of states reorganizes into a band. We show that this occurs at order 2s in perturbation theory. The ground state is non-degenerate for integer spin, but degenerate for half-odd integer spin as is required by Kramers' theorem [18].     

Incommensurate phases in ferromagnetic spin-chains with weak antiferromagnetic interchain interaction

We study planar ferromagnetic spin-chain systems with weak antiferromagnetic inter-chain interaction and dipole-dipole interaction. The ground state depends sensitively on the relative strengths of antiferromagnetic exchange and dipole energies κ = J′a ² c/(g _L μ _B )². For increasing values of κ, the ground state changes from a ferromagnetic via a collinear antiferromagnetic and an incommensurate phase to a 120° structure for very large antiferromagnetic energy. Investigation of the magnetic phase diagram of the collinear phase, as realized in CsNiF₃, shows that the structure of the spin order depends sensitivly on the direction of the magnetic field in the hexagonal plane. For certain angular domains of the field incommensurate phases appear which are seperated by commensurate phases. When rotating the field, the wave vector characterizing the structure changes continously in the incommensurate phase, whereas in the commensurate phase the wave vector is locked to a fixed value describing a two-sublattice structure. This is a result of the competition between the exchange and the dipole-dipole interaction.