Spin transport in a one-dimensional anisotropic Heisenberg model

We analytically and numerically study spin transport in a one-dimensional Heisenberg model in linear-response regime at infinite temperature. It is shown that as the anisotropy parameter Δ is varied spin transport changes from ballistic for Δ<1 to anomalous at the isotropic point Δ=1, to diffusive for finite Δ>1, ending up as a perfect isolator in the Ising limit of infinite Δ. Using perturbation theory for large Δ a quantitative prediction is made for the dependence of diffusion constant on Δ.     

Quasi-one-dimensional anisotropic Heisenberg model in a transverse magnetic field

The phase diagram of weakly coupled XXZ chains in a transverse magnetic field is studied using the mean-field approximation for the interchain coupling and known exact results for an effective one-dimensional model. The results are applied to the quasi-one-dimensional antiferromagnet Cs₂CoCl₄, and the value of interchain interaction in this compound is estimated.     

Swap action in a solid-state controllable anisotropic Heisenberg model

Correct swap action can be realized via the control of the anisotropic Heisenberg interaction in solid-state quantum systems. The conditions of performing a swap are derived by the dynamics of arbitrary bipartite pure state. It is found that swap errors can be eliminated in the presence of symmetric anisotropy. In realistic quantum computers with unavoidable fluctuations, the gate fidelity of swap action is estimated. The scheme of quantum computation via the anisotropic Heisenberg interaction is implemented in a one-dimensional quantum dots. The slanting and static magnetic field can be used to adjust the anisotropy.     

On stationary topological solitons in a two-dimensional anisotropic Heisenberg model

We study stationary two-dimensional solitons in an easy-axis Heisenberg magnet with the Hamiltonian density wherei=1, 2,a=1, 2, 3, and (x _i ) is the angle between unit vector s(x _i ) and the easy axis, 0<p<. Stable solitons with a topological chargeQ=1 and localized distributionss ^a (x _i ) withQ=2 are found. The existence of the bound states of two solitons withQ=1 is shown numerically for 0<p<.     

Green functions of the anisotropic Heisenberg model

The Green functions of the anisotropic Heisenberg model are studied by a method which was applied previously to the reduced density matrices. Integral equations are used to prove the existence of the infinite volume limit of the Green functions, and some analyticity properties with respect to the fugacity (or magnetic field), the potentials, and the complex times.Research supported by the National Science Foundation.     

Spin-density functional for exchange anisotropic Heisenberg model

Ground-state energies for antiferromagnetic Heisenberg models with exchange anisotropy are estimated by means of a local-spin approximation made in the context of the density functional theory. Correlation energy is obtained using the non-linear spin-wave theory for homogeneous systems from which the spin functional is built. Although applicable to chains of any size, the results are shown for small number of sites, to exhibit finite-size effects and allow comparison with exact-numerical data from direct diagonalization of small chains.     

The anisotropic Heisenberg model in the long-range interaction limit

We consider the general spin quantum mechanical anisotropic Heisenberg model on av-dimensional lattice with potential γ ^v ?(γ|r|) of Kac type. In the limit γ→0+ (after the thermodynamic limit) it is shown that the free energy is equivalent to the corresponding Curie-Weiss or mean-field expression.     

Dimer state in the two-dimensional anisotropic alternated-exchange Heisenberg model

An analysis is made of the two-dimensional Heisenberg model with S=1/2, anisotropic exchange interaction between nearest neighbors, and alternating exchange in two directions, [100] and [010] (corresponding to condensation of the (π, π) mode) and in one direction [100] (corresponding to condensation of the (π, 0) mode). The quantum Monte Carlo method is used to calculate the thermodynamic characteristics and the spin correlation functions which are used as the basis to determine the boundary of stability of an anisotropic antiferromagnetic with respect to alternation of exchange δ=(1−J ^x,y /J ^z )^0.4 in the (π,π) model and δ=(1−J ^x,y /J ^z )^0.31 in the (π,0) model. In the (π,0) model a disordered quantum state exists in the range (1−J ^x,y /J ^z )^0.31<δ<(0.3–0.35). The energy (E−0.68)=0.36δ ^1.80(6) and 0.21 δ ^2.0(5), the energy gap between the ground and excited states H _c (δ)=1.96δ ^2.(1), 1.8(1) (δ−0.35(3))^0.67(2) were determined as a function of the alternation of exchange in the (π,π)-and (π,0) models, respectively. Fiz. Tverd. Tela (St. Petersburg) 40, 1080–1085 (June 1998)     

One-dimensional anisotropic Heisenberg model in the transverse magnetic field

The one-dimensional spin-1/2 XXZ model in a transverse magnetic field is studied. It is shown that the field induces a gap in the spectrum of the model with the easy-plane anisotropy. Using conformal invariance, the field dependence of the gap is found at small fields. The ground state phase diagram is obtained. It contains four phases with the long-range order of different types and a disordered phase. These phases are separated by critical lines, where the gap and the long-range order vanish. Using scaling estimates, the mean-field approach, and numerical calculations in the vicinity of all critical lines, we find the critical exponents of the gap and the long-range order. It is shown that the transition line between the ordered and disordered phases belongs to the universality class of the transverse Ising model.     

Hysteresis behavior of the anisotropic quantum Heisenberg model

The effect of the anisotropy in the exchange interaction on the hysteresis loops within the anisotropic quantum Heisenberg model has been investigated with the effective field theory for two spin cluster. Particular attention has been devoted on the behavior of the hysteresis loop area, coercive field and remanent magnetization with the anisotropy in the exchange interaction for both ferromagnetic and paramagnetic phases.     

Reduced density matrices of the anisotropic Heisenberg model

The reduced density matrices of the anisotropic Heisenberg model are studied by means of a functional integral representation based on a generalized Poisson process. Integral equations, which are analogous to the classical Kirkwood-Salzburg equations, are then used to prove the existence of the infinite volume limit of the reduced density matrices, analyticity properties with respect to the fugacity (or magnetic field) and the potentials, and a cluster property, in the low fugacity (high magnetic field) region.The research reported in this paper was supported by the National Science Foundation.     

Long range order in the anisotropic quantum ferromagnetic Heisenberg model

We study the anisotropic quantum mechanical ferromagnetic Heisenberg model. By anisotropic we mean that thex andy exchange constants are equal but smaller than thez exchange constant. We show that for any amount of anisotropy there is long range order in two or more dimensions at low enough temperature. We also develop a convergent low temperature expansion and use it to prove exponential decay of the truncated correlation functions.Research partially supported by U.S. National Science Foundation under Grant PHY8116101 AO 3     

A variational approach for the classical anisotropic Heisenberg model in a crystal field

The variational approach based on the Bogoliubov inequality for the free energy is used to study the three-dimensional anisotropic Heisenberg XXZ model with a crystal field. The magnetization and the phase diagrams are obtained as a function of the parameters of the Hamiltonian. Limiting cases, such as isotropic Heisenberg, XY, and planar rotator models in two and three dimensions, are analyzed and compared to previous results obtained from analytical approximations as well as to those obtained from more reliable approaches such as series expansion and Monte Carlo simulations. A parametric procedure has been used in order to simplify the solutions of the self-consistent coupled equations.     

A constant-magnetization ensemble for the classical anisotropic Heisenberg model

A constant-magnetization ensemble is introduced in order to study classical, anisotropic Heisenberg systems. Existence, uniform convergence, and convexity properties are proved for an appropriate thermodynamic potential. The thermodynamic equivalence of this ensemble with the more common canonical ensemble is also established. In a subsequent paper, this formulation is used to obtain an exact statistical mechanical solution of classical Heisenberg systems with long-range Kac interactions.This research was carried out at The Department of Physics, Case Western Reserve University, Cleveland, Ohio, and was supported in part by the U.S. Atomic Energy Commission. This work is based on portions of a dissertation by K. M. submitted in partial fulfillment of the Ph.D. degree, Case Western Reserve University.     

Green function approach to an anisotropic to an anisotropic Heisenberg model with mixed spins

Green function technique with random phase approximation has been utilized to obtain the Curie temperature of a mixed spin system for an anisotropic Heisenberg model with uniaxial anisotropy. The results obtained have been compared with the isolated spin system of a regular lattice.     

Spin-peierls transition in anisotropic Heisenberg chains

We study spin-Peierls transition for anisotropic Heisenberg chains within mean field theory. We find that dimerization occurs in the absence of a magnetic field and when the field is smaller than a critical field H_c. The transition temperature is obtained as a function of anisotropy and magnetic field.     

Nonlinear spin excitations in a classical Heisenberg anisotropic helimagnet

The nonlinear spin excitations in an anisotropic helimagnet in the presence of a constant magnetic field are investigated in the classical continuum limit. The helical character is introduced into the model, in analogy with the twist in a cholesteric liquid crystal. After deriving a class of spin wave solutions for the stereographic representation of the Landau-Lifshitz equation, in-plane stationary spin configurations are obtained and their stability is analysed. When the external magnetic field is along the anisotropic axis, modulational instability is observed in the spin lattice, and when the external magnetic field is normal to the anisotropic axis, the spin configurations are unstable. The perturbed spin components show fluctuations in the tail region, while the velocity and amplitude of the soliton remain unaltered.     

Finite temperature dynamics of vortices in the two dimensional anisotropic Heisenberg model

We study the effects of finite temperature on the dynamics of non-planar vortices in the classical, two-dimensional anisotropic Heisenberg model with XY- or easy-plane symmetry. To this end, we analyze a generalized Landau-Lifshitz equation including additive white noise and Gilbert damping. Using a collective variable theory with no adjustable parameters we derive an equation of motion for the vortices with stochastic forces which are shown to represent white noise with an effective diffusion constant linearly dependent on temperature. We solve these stochastic equations of motion by means of a Green's function formalism and obtain the mean vortex trajectory and its variance. We find a non-standard time dependence for the variance of the components perpendicular to the driving force. We compare the analytical results with Langevin dynamics simulations and find a good agreement up to temperatures of the order of 25% of the Kosterlitz-Thouless transition temperature. Finally, we discuss the reasons why our approach is not appropriate for higher temperatures as well as the discreteness effects observed in the numerical simulations. Received: 27 April 1998 / Revised: 2 September 1998 / Accepted: 10 September 1998