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Natural Science

Excitations for the one-dimensional S = 1 pseudo-Heisenberg antiferromagnetic chain

E. V. Orlenko, Fedor E. Orlenko, George G. Zegrya

Published Jan 1, 2010• 1 citation
Publisher

Abstract

We are interested in the anisotropic S=1 antiferromagnetic chain. System of particles with an arbitrary spin is described directly from the first principles, based on the symmetry law. The ground state of the one-dimensional S=1 pseudo-Heisenberg antiferromagnet with single-ion anisotropy is calculated. Excitations of the chain in the form of nonlinear spin waves and, in particular, the possibility of a soliton solution is considered.

DOI
10.4236/ns.2010.211155

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We are interested in the anisotropic S=1 antiferromagnetic chain. System of particles with an arbitrary spin is described directly from the first principles, based on the symmetry law. The ground state of the one-dimensional S=1 pseudo-Heisenberg antiferromagnet with single-ion anisotropy is calculated. Excitations of the chain in the form of nonlinear spin waves and, in particular, the possibility of a soliton solution is considered.
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 calculate energies and wave functions of S=1 antiferromagnetic Heisenberg chains with single-ion anisotropy in a symmetry-breaking external magnetic field. From results for the string correlation function for low-lying excited states we identify these states as solitons with respect to the hidden string order. For finite anisotropic chains we investigate the transition to the fully magnetized state at high magnetic fields and conclude that Bose condensation in an external magnetic field occurs also for the anisotropic chain.
A spin-1 antiferromagnetic Heisenberg chain with a single-ion anisotropy Dtsumj{\mathit{Dtsum}}_{\mathit{j}}Dtsumj​(Sjz{\mathit{S}}_{\mathit{j}}^{\mathit{z}}Sjz​)2{)}^{2})2 is investigated on the basis of the continuum representation of the model Hamiltonian. Analytical results for the ground state, the excitation spectrum, and the correlation functions are derived in a self-consistent-field approach. We find that the ground state is made of boson pairs and the correlation functions in the ground state decay exponentially. Two Haldane gaps due to the single-ion anisotropy are obtained and a transition at the critical value Dc{\mathit{D}}_{\mathit{c}}Dc​=1 is shown in the lower Haldane gap and the correlation functions.
We study the ground-state phase diagram and the excitations of a one-dimensional s=1 Heisenberg antiferromagnet including exchange and single ion anisotropy with anisotropy constants \ensuremath{\epsilon} and D, respectively. Starting from the ground state for D=\ensuremath{\infty}, a new class of spin-one defects is introduced. Treating these defects as fermions and performing a mean-field approximation, we find three phases: the N\'eel, the Haldane, and the large-D phase. The corresponding phase diagram is partly in good agreement with existing data. The N\'eel and the string order parameters have the correct behavior in the large-D and the Haldane phase, but not in the N\'eel phase. For a certain variational state, we find a ground-state energy which perfectly agrees with the best quantum Monte Carlo data. Finally we argue that the low-lying one-particle excitations are of fermionic character.
Effective nonlinear field theory for a semiclassical long-wavelength description of one-dimensional S=1/2 Heisenberg antiferromagnets with dimerized ground states is derived within an approach using two-site coherent states. The method is applied to bond-alternating anisotropic spin chains in presence of external magnetic field and next-nearest-neighbor interactions. Linear and nonlinear excitations in singlet and magnetic phases are studied. Soliton solutions are found and their properties under semiclassical quantization are discussed. \textcopyright{} 1996 The American Physical Society.
The ground state and low-lying excited states of a one-dimensional Heisenberg model with axial anisotropy are studied by extrapolation from finite lattices. The ground-state properties and the phase diagram are determined for quantum spins, especially for S=12,1,and32S=\frac{1}{2}, 1, \mathrm{and} \frac{3}{2}S=21​,1,and23​. Higher spin values do not give new features in the phase diagram. the limitations of finite-lattice extrapolation are discussed in connection with the possibility of a singlet phase for the S=1S=1S=1 isotropic Heisenberg antiferromagnet.