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Journal of Physics C Solid State Physics

On solitons in semiclassical limit of the quantum spin1/2Heisenberg chain

A Popielewicz

Published Apr 20, 1981• 1 citation
Publisher

Abstract

Using the exact Goldhirsch (1980) boson expansion of spin 1 / 2 operators and coherent states representation the author obtains an exact semiclassical equation of motion for the anisotropic Heisenberg chain. Comparison is made with the classical case and with other approaches in the quantum case. The possible contribution to the quasi-elastic neutron scattering cross section is estimated.

DOI
10.1088/0022-3719/14/11/009

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Using the exact Goldhirsch (1980) boson expansion of spin 1 / 2 operators and coherent states representation the author obtains an exact semiclassical equation of motion for the anisotropic Heisenberg chain. Comparison is made with the classical case and with other approaches in the quantum case. The possible contribution to the quasi-elastic neutron scattering cross section is estimated.
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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 spin-coherent states as the basis of a time-dependent variational ansatz for a semiclassical description of a large family of Heisenberg models. In addition to following common approaches we also evaluate the square variance of the Hamiltonian in terms of coherent states. This quantity turns out to have a natural interpretation with respect to time-dependent solutions of the equations of motion and allows an estimate of quantum fluctuations in a semiclassical regime to be made. The general results are applied to solitons, instantons and vortices in several one- and two-dimensional models.