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Physical review. B, Condensed matter

Nonlinear excitation in anS=1/2 Heisenberg ferromagnetic chain

Zhu-Pei Shi

Published Feb 1, 1992• 3 citations
Publisher

Abstract

Nonlinear excitations in an S=1/2 Heisenberg ferromagnetic chain are investigated by using the squeezed fermion coherent states and the Jordan-Wigner fermionic transformation of spin-1/2 operators. The equation of motion for a fermion operator is a modified Schr\"odinger equation. Solitonlike excitations are obtained, and their spectrum has a linear dispersion at low energies.

DOI
10.1103/physrevb.45.2502

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Nonlinear excitations in an S=1/2 Heisenberg ferromagnetic chain are investigated by using the squeezed fermion coherent states and the Jordan-Wigner fermionic transformation of spin-1/2 operators. The equation of motion for a fermion operator is a modified Schr"odinger equation. Solitonlike excitations are obtained, and their spectrum has a linear dispersion at low energies.
From the point of view of the quantum lattice liquid, an attempt is made to understand the nonlinear solitonlike excitations in the quantum anisotropic Heisenberg chain with the help of the coherent-state method. It is argued that the modified terms of the nonlinear Schr\"odinger equation are strongly restricted by the relation between the continuum approximation and the semiclassical approximation represented by two smallness parameters \ensuremath{\eta} and \ensuremath{\epsilon}, respectively. When assuming that \ensuremath{\eta} and \ensuremath{\epsilon} are of the same order (\ensuremath{\eta}\ensuremath{\sim}\ensuremath{\epsilon}), after retaining terms of order O(${\mathrm{\ensuremath{\epsilon}}}^{6}$), the equation of motion of the Bose operators satisfies the cubic nonlinear Schr\"odinger equation. Envelope-kink excitations and energy gaps are obtained. Some relevant physical results are also discussed.
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.
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.
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.