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Journal of Physics C Solid State Physics

Solitary waves in a 1D isotropic Heisenberg ferromagnet

L G de Azevedo, M. A. De Moura, Chiara Delpiano Cordeiro, Boštjan Žekš

Published Dec 30, 1982• 33 citations
Publisher

Abstract

The authors present the derivation of a non-linear Schrodinger equation for the quantum isotropic Heisenberg chain using the coherent-states method combined with the Holstein-Primakoff bosons representation of the spin operator. The solution of this equation gives rise to solitary-waves excitations of the system that are similar to those discussed by Tjon and Wright (1977) for the classical Heisenberg chain. A discussion of their results as compared with others in the literature is made.

DOI
10.1088/0022-3719/15/36/020

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The authors present the derivation of a non-linear Schrodinger equation for the quantum isotropic Heisenberg chain using the coherent-states method combined with the Holstein-Primakoff bosons representation of the spin operator. The solution of this equation gives rise to solitary-waves excitations of the system that are similar to those discussed by Tjon and Wright (1977) for the classical Heisenberg chain. A discussion of their results as compared with others in the literature is made.
Using the coherent states method combined with the Schwinger coupled boson representation of the spin operators (1965) it is shown that solitons can propagate in the continuum limit of the quantum ferromagnetic Heisenberg chain. These solitons are solutions of a nonlinear Schrodinger equation similar to that discussed by Lakshmanan (1977) for the classical Heisenberg chain. Several characteristics of the soliton, like its momentum, energy, and the number of bosonic excitations involved in the soliton formation, are calculated.
The spin evolution equation of an isotropic, quantum ferromagnetic Heisenberg chain is analyzed in the continuum approximation using spin-coherent states. The advantages of this approach are discussed. Magnetic solitary-wave solutions are found, and the expectation values of the energy, momentum, and angular momentum corresponding to these solutions are determined. The energy-momentum dispersion relation for the nonlinear excitations is derived. The semiclassical spectrum is shown to arise when quantum effects are neglected by using a random-phase approximation to calculate certain expectation values. On including the quantum effects, it is found that the spectrum comprises two branches: a lower-energy branch of spin-wave-like, small-amplitude solitary waves with small quantum corrections, and a higher branch of particlelike large-amplitude solitary waves subject to significant quantum corrections for small S values. A heuristic discussion of the stability of these excitations is presented. A physical interpretation of the dispersion relation obtained is given.
An anisotropic Heisenberg ferromagnetic spin chain model is studied by using Holstain-Primakoff representation. In the semiclassical limit, the exact solutions for bright and dark solitons are found by using the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators. These results show that the solutions can be expressed in terms of the elliptic integrals in different parameter regions. Some solutions for dark solitons are the innovation points in this paper.
We use a spin-coherent representation to derive the spectrum of nonlinear excitations in a spin-S quantum ferromagnetic Heisenberg chain in the continuum limit. Quantum effects split the semiclassical spectrum into two branches---a lower branch of spin-wave-like, large-width solitary waves with negligible quantum corrections for all S, and an upper branch of particlelike, small-width solitary waves subject to significant quantum corrections for low S. The stability of these excitations is briefly discussed.