Haldane gap in the S = 1 Haldane-Shastry model

We present evidence that the S = 1 Haldane- Shastry model has a gap in the energy spectrum, extending to the case of a model with long-range interactions results previously obtained by Haldane and, numerically, by other authors for the case of short-range interactions. We studied the groundstate and first excited state using a modified Lanczos algorithm and obtained the low temperature behavior diagonalizing exactly small chains. The correlation functions decay exponentially with distance and the low-T susceptibility decays exponentially to zero. The gap is larger than for the Heisenberg model and the correlation functions decay faster indicating a smaller correlation length.     

Finite-size effects in a field-theoretic model with long-range exchange interaction

We present a systematic approach to the calculation of finite-size (FS) effects for anO(n) field-theoretic model with both short-range (SR) and long-range (LR) exchange interactions. The LR exchange interaction decays at large distances as 1/r ^d+2–2,0⁺,0⁺. Renormalization group calculations ind=d _u – are performed for a system with a fully finite (block) geometry under periodic boundary conditions. We calculate the FS shift of the critical temperature and the FS renormalized coupling constant of the model to one-loop order. The universal scaling variable is obtained and the FS scaling hypothesis is verified.     

Effect of a staggered magnetic field on the S=1 Haldane chain with single-ion anisotropy

We analyze the gaps in the excitation spectrum of a Haldane chain with single-ion anisotropy in a staggered field. We show that the gap along the direction of the field increases at a faster rate than the others, while its spectral weight decreases, being transferred to a two-magnon continuum.     

Investigation of the magnetic properties of chains with alternating ferro-and antiferromagnetic exchange interactions in the Heisenberg model with spin S=1/2

The quantum Monte Carlo method is used to calculate the susceptibility and pairwise spin-spin correlation functions of chains with alternating ferro (K)-and antiferromagnetic (J)-exchange interactions within the Heisenberg model with spin S=1/2. From the susceptibility, the energy gap between the ground state and excited triplet states is determined or arbitrary ratios K/J. The value of the gap coincides with the Haldane gap for spin S=1 when K/J>1.25. Fiz. Tverd. Tela (St. Petersburg) 41, 1650–1651 (September 1999)     

Spin-ordering in S = 1 anisotropic Heisenberg models with nondiagonal spin exchange

The properties of S = 1 anisotropic Heisenberg models with nondiagonal exchange between axial and planar spin components are investigated using Monte Carlo techniques. The quantum nature is taken into account in a semi-classical approximation. The ordering of the spins when applying an external field with axial and planar components is discussed. It is argued that the quantum nature of the spins and the nondiagonal exchange may explain the peculiar shape of the magnetic specific heat of FeBr₂ as well as the weakly first-order phase transition observed in the same compound when a tilted field is applied. Received 24 January 1999     

Artificial Haldane gap material on a semiconductor chip

We show how nanostructuring of a metallic gate of a field-effect transistor (FET) converts the electron channel of an FET to an artificial Haldane chain with a gap in the energy spectrum. A specially designed gate structure creates a chain of triple quantum dot molecules. The electrons localized in the molecules realize a spin-half Heisenberg chain with spin–spin interactions alternating between ferromagnetic and antiferromagnetic. The quantum state of an FET is a semiconductor implementation of an integer spin-one antiferromagnetic Heisenberg chain with a unique correlated ground state and a finite energy gap, originally conjectured by Haldane.     

Phase diagram in the quantum XY model with long-range interactions

We study the d-dimensional quantum XY model with ferromagnetic long-range interaction decaying as r-p in terms of boson operators, by employing the coherent state path integral approach. We have obtained a finite critical temperature as a function of the dimension (d) for d2d the system becomes disordered at all temperatures. For the particular values p=3/2 and d=1 our theoretical calculations are comparable to those from Monte Carlo simulations.     

Entanglement in a two-spin system with long-range interactions

The quantum entanglement between two spins in the Ising model with an added Dzyaloshinsky–Moriya(DM) interaction and in the presence of the transverse magnetic field is studied. The exchange interaction is considered as a function of the distance between spins. The negativity as a function of magnetic field, exchange and DM interaction is calculated.The effect of the distance between spins is studied based on the negativity. In addition, the effect of the thermal fluctuation on the negativity is also investigated.     

Weakly nonextensive thermostatistics and the Ising model with long-range interactions

We introduce a new nonextensive entropic measure that grows like , where N is the size of the system under consideration. This kind of nonextensivity arises in a natural way in some N-body systems endowed with long-range interactions described by interparticle potentials. The power law (weakly nonextensive) behavior exhibited by is intermediate between (1) the linear (extensive) regime characterizing the standard Boltzmann-Gibbs entropy and (2) the exponential law (strongly nonextensive) behavior associated with the Tsallis generalized q-entropies. The functional is parametrized by the real number in such a way that the standard logarithmic entropy is recovered when . We study the mathematical properties of the new entropy, showing that the basic requirements for a well behaved entropy functional are verified, i.e., possesses the usual properties of positivity, equiprobability, concavity and irreversibility and verifies Khinchin axioms except the one related to additivity since is nonextensive. For , the entropy becomes superadditive in the thermodynamic limit. The present formalism is illustrated by a numerical study of the thermodynamic scaling laws of a ferromagnetic Ising model with long-range interactions. Received 24 May 2000     

Nonequilibrium tricritical point in a system with long-range interactions

Systems with long-range interactions display a short-time relaxation towards quasistationary states whose lifetime increases with system size. With reference to the Hamiltonian mean field model, we here show that a maximum entropy principle, based on Lynden-Bell's pioneering idea of "violent relaxation," predicts the presence of out-of-equilibrium phase transitions separating the relaxation towards homogeneous (zero magnetization) or inhomogeneous (nonzero magnetization) quasistationary states. When varying the initial condition within a family of "water bags" with different initial magnetization and energy, first- and second-order phase transition lines are found that merge at an out-of-equilibrium tricritical point. Metastability is theoretically predicted and numerically checked around the first-order phase transition line.     

Magnetization and compensation temperature of transition-metal–rare-earth multilayers in a model with long-range interactions

A model is proposed to describe the behavior of magnetization and compensation temperature in transition-metal–rare-earth multilayers. Long-range exponentially decreasing ferromagnetic (antiferromagnetic) interactions are considered between the same (different) kind of atoms. The magnetization and compensation temperature are shown to decrease with increasing single layer thickness. Good agreement is obtained with experimental data on Tb/Co system.