It is shown that the equation of motion for the classical continuous Heisenberg spin chain with uniaxial anisotropy is obtained as a reduction of the two-component derivative nonlinear Schrodinger equation.
In the recent literature, there have been discussions of nonlinear spin excitations in one-dimensional, anisotropic Heisenberg spin chains. These have the character of localized excitations, which emerge from the time-dependent classical equations of motion. We show that for a given frequency, in a finite spin chain one has a hierarchy of nonlinear excitations, whose envelopes have the appearance of a one soliton, two soliton,..., states. Also, we consider the nature of these nonlinear excitations in an applied magnetic field of frequency \ensuremath{\omega}, and explore aspects of the transient behavior of the system in response to a time varying external field. \textcopyright{} 1996 The American Physical Society.
One-dimensional spin chains are investigated by constructing a mapping of the anisotropic Heisenberg model in the limit Delta to 1 onto the non-linear Schrodinger model (a gas of bosons with delta function interactions). Three applications of this mapping are given. First it is shown that the Bethe ansatz solutions of the anisotropic spin-1/2 Heisenberg model go over to the continuous Bethe ansatz solutions of the non-linear Schrodinger model. Then bound-state energies for arbitrary spin are calculated and as a third application a nearly identical mapping of the anisotropic spin-1/2 Heisenberg model in the limit Delta to 0 onto a non-linear Schrodinger model for fermion fields is given. Finally the authors construct an anisotropic SU(N) model. The continuum limit of this model is shown to be the (N-1)-component non-linear Schrodinger model, which can be solved by means of the nested Bethe ansatz.
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.