Antiferromagnetic Quantum Spin Chains Research Articles

Effects of randomness in gapped antiferromagnetic quantum spin chains

The effects of bond randomness are studied for spin chains with excitation gaps in the pure case. Systems with enforced topological structure like the spin-1/2 chain with enforced dimerization and spin-1 chain in the Haldane gapped phase appear very stable against randomness. On the other hand, systems with spontaneously generated topological order like the spin-1/2 chain with spontaneous dimerization are found to be unstable even for weak randomness despite the gap.

Testing Haldane's conjecture in the O(3) model by a meron cluster simulation

Twelve years ago, Haldane formulated his famous conjecture for 1-d antiferromagnetic quantum spin chains. In the context of the 2-d O(3) model with a \theta term, it predicts a phase transition at \theta = \pi, which has not yet been verified reliably. To simulate this we use the Wolff cluster algorithm together with an improved estimator for the topological charge distribution. Each cluster carries integer or half integer charge. Clusters with charge 1/2 are identified with merons. At \theta = \pi they are inactive, such that the mass gap vanishes. We obtain critical exponents which are consistent with predictions from the k=1 WZNW model, therefore confirming a second order phase transition.

Meron-cluster simulation of the theta vacuum in the 2D O(3) model.

The 2D O(3) model with a $\ensuremath{\theta}$ vacuum term is formulated in terms of Wolff clusters. Each cluster carries an integer or half-integer topological charge. The clusters with charge \ifmmode\pm\else\textpm\fi{}\textonehalf{} are identified as merons. At $\ensuremath{\theta}=\ensuremath{\pi}$ the merons are bound in pairs inducing a second order phase transition at which the mass gap vanishes. The construction of an improved estimator for the topological charge distribution makes numerical simulations of the phase transition feasible. The measured critical exponents agree with those of the $k=1$ Wess-Zumino-Novikov-Witten (WZNW) model. Our results are consistent with Haldane's conjecture fro 1D antiferromagnetic quantum spin chains.

Quantum solitons and the Haldane phase in antiferromagnetic spin chains

A survey is given of the relevance of solitons for the present understanding of antiferromagnetic quantum spin chains. For the S = 1 2 xxz -chain the basic elementary excitations are solitons. Two solitons combine to form a magnon and its internal degree of freedom is observed as an excitation continuum. For S = 1 chains the existence of the massive Haldane phase is related to the dissociation of soliton pairs (pairs of domain walls with respect to antiferromagnetic order). Based on the hidden (or string) order, the appropriate mean field theory for antiferromagnetic S = 1 chains is introduced as based on uncorrelated solitons and applied to calculate correlation functions. It is described how to include correlations between solitons using an approximate mapping to an effective S = 1 2 chain. The basic elementary excitations in the Haldane phase are identified as solitons with respect to the hidden order.

Thermodynamic properties of the Δ-chain model in a uniform magnetic field

A numerical approach for calculating an eigenvalue distribution function is developed and it is applied to the study on a fully frustrated spin system called the \ensuremath{\Delta}-chain model. We examine the magnetic-field dependence of the specific heat to clarify the relationship between the highly frustrated spins and the lower-temperature peak which has been extensively investigated by Kubo. Our numerical data show that with the increase of magnetic field, the peak width becomes broader and the height lower. This sensitive dependence should be caused by lowering the high degeneracy of states contributing to the peak formation. On the other hand, we also find that the higher-temperature peak observed commonly in antiferromagnetic quantum spin chains is almost unchanged.

SCALAR KINKS

We determine the excitations and S matrix of an integrable isotropic antiferromagnetic quantum spin chain of alternating spin 1/2 and spin 1. There are two types of gapless one-particle excitations: the usual spin 1/2 (“spinor”) kink, and a new spin 0 (“scalar”) kink. Remarkably, the scalar-spinor scattering is nontrivial, yet the spinor-spinor scattering is the same as for the Heisenberg chain. Moreover, there is no scalar-scalar scattering.

Bethe-Ansatz Approximation for theS=1 Antiferromagnetic Spin Chain

We introduce an approximation scheme where the Bethe ansatz is applied to non-integrable systems: the many-body S matrix is approximated by a product of two-body S matrices. We call this method Bethe-ansatz approximation (BAA). We apply the BAA to the S =1 antiferromagnetic bilinear-biquadratic quantum spin chain. The model contains a parameter β , the ratio of the biquadratic coupling to the bilinear coupling. Except for β=-∞ , ±1, the system is non-integrable. Varying β , we performed BAA calculation of the ground-state energy as a function of the total magnetization. Comparison with the numerical diagonalization shows a considerable efficiency of the BAA up to medium or more particle density.

Edge states in antiferromagnetic quantum spin chains.

The structure of edge states in general finite antiferromagnetic quantum spin chains with arbitrary spin value S is discussed within the framework of the nonlinear-sigma model (NL\ensuremath{\sigma}M) plus a topological \ensuremath{\theta} term. Based on a large-N theory of SU(N) quantum antiferromagnets and strong-coupling expansion, we argue that edge states with fractionalized spin quantum number S' exist in all spin chains with S\ensuremath{\ge}1, with S'=S/2 for integer spin chains and S'=(S-1/2)/2 for half-integer spin chains.

The spectra of q-state vertex models and related antiferromagnetic quantum spin chains

Some exactly solvable q-state vertex models are investigated. The author employs inversion relations to determine directly the spectra of the transfer matrices in the thermodynamic limit by avoiding the more cumbersome Bethe Ansatz. The results are applied to related quantum spin chains of which two families are SU(q) and SO(q) invariant, respectively. Various quantities are calculated, e.g. energy-momentum excitations and the correlation length. For q=3 the SU(q) invariant chain is the pure biquadratic spin-1 Hamiltonian which turns out to be non-critical. The ground-state energy, the gap, and the correlation length are given.

Random exchange effects in antiferromagnetic quantum spin chains: A Monte Carlo study

We have carried out Monte Carlo studies of a random-exchange antiferromagnetic spin-(1/2) chain. For systems with XY-like (anisotropic) and with Heisenberg (isotropic) coupling, our results confirm the existence of a disorder-induced low-temperature (T) divergence in the long-wavelength ${S}^{z}$-${S}^{z}$ susceptibility \ensuremath{\chi} which was previously predicted by real-space renormalization-group (RSRG) treatments. Over the finite temperature range studied, these results are consistent with a 1/(T ${\mathrm{ln}}^{2}$T) behavior of \ensuremath{\chi}, and hence in qualitative agreement with the RSRG results. As in the XY-Heisenberg regime, we also find a disorder-induced enhancement of the low-T susceptibility for a system with Ising-like exchange coupling which, over the finite temperature range studied, is again consistent with RSRG results. However, there are inconsistencies between the RSRG predictions in the Ising-like regime at very low temperatures, and the exact results for the random-exchange Ising chain and the low-temperature behavior of \ensuremath{\chi} in the Ising-like regime may in fact be more complicated than predicted by RSRG. Finally, we also present results for the antiferromagnetic susceptibility and structure factor. For both Heisenberg and Ising-like systems, we find that disorder suppresses the long-range antiferromagnetic correlations at low T.