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Journal of Applied Physics

Soliton spin configurations along the classical anisotropic Heisenberg chain

Bruce D. Gaulin

Published Apr 15, 1987• 7 citations
Publisher

Abstract

The spin configurations of a one-dimensional, weakly anisotropic Heisenberg antiferromagnet were examined by means of an importance sampling Monte Carlo simulation. The spin interactions display weak anisotropies of the same form in each of the orthogonal XY and XZ planes. This allows for two soliton modes, with one in each of the planes. The soliton density within the XZ plane has been determined as a function of the relative strengths of the two anisotropies as well as of temperature. These results are compared with theoretical analysis of similar systems.

DOI
10.1063/1.338401

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The spin configurations of a one-dimensional, weakly anisotropic Heisenberg antiferromagnet were examined by means of an importance sampling Monte Carlo simulation. The spin interactions display weak anisotropies of the same form in each of the orthogonal XY and XZ planes. This allows for two soliton modes, with one in each of the planes. The soliton density within the XZ plane has been determined as a function of the relative strengths of the two anisotropies as well as of temperature. These results are compared with theoretical analysis of similar systems.
We study the quantum-statistical mechanics, at low temperatures, of a one-dimensional antiferromagnetic Heisenberg model with two anisotropies. In the weak-coupling limit we determine the temperature dependences of the soliton energy and the soliton density. We have found that the leading correction to the sine-Gordon (SG) expression for the soliton density and the quantum soliton energy comes from the out-of-plane magnon mode, not present in the pure SG model. We also show that when an external magnetic field is applied, the chain supports a new type of kink, where the sublattices rotate in opposite directions.
An important sampling Monte Carlo method is used to study the classical, antiferromagnetic, XY chain in a symmetry breaking uniform magnetic field. From equilibrium configurations we extract values for the bulk properties as well as explicit pictures showing individual spin directions. An analysis of the angles which the spin makes with the field shows clearly the presence of both ‘‘π-like’’ and ‘‘2π-like’’ solitons. We also see two distinct types of ‘‘π-like’’ solitons which differ in their behavior as a function of field. The bulk properties are discussed in terms of both spin waves and soliton excitations.
We have studied two models for anisotropic quantum spin chains. (i) XY-chain with a field in the plane: The magnetization of the ferromagnet behaves as h1/3 for small fields, in agreement with scaling laws. The antiferromagnet shows a critical field at which the ground state is a simple Néel state and which separates power law from exponential decay of spatial correlations. (ii) Anisotropic XY-chain: The dynamic z-component spin correlation function can be decomposed into a spin wave and a soliton contribution. The nature of quantum soliton excitations is studied and their form compared to soliton solutions of classical equations of motion.
We study the phase diagram of the three-dimensional classical ferromagnetic Heisenberg model with an easy-plane crystalline anisotropy and an easy-axis exchange anisotropy through Monte Carlo simulations. We employ the Metropolis algorithm together with single-histogram techniques in order to characterize the transitions in each region of the phase diagram. Our results reveal, besides the disordered phase, the existence of Ising-like and XY-like ordered phases which are separated by a first-order transition line.
Elementary excitations are studied near the Ising limit close to the degenerate point in the one-dimensional anisotropic Heisenberg antiferromagnets with up to next-nearest-neighbor interactions. Solitons in the Néel and (2,2) antiphase states and triplet-dimer excitations in the dimer state are found as propagating modes. These excitations are found to dominate the shape of the central peak in dynamical spin correlation functions, through the comparison with the numerical results by an exact diagonalization method for finite chains. The temperature dependence of the static correlation function is also discussed, and the shape is found to change gradually with increasing temperature, approaching the zero-temperature correlation function at the degenerate point.