From Magnons to Solitons
This article concerns magnetism in nonmetallic solids. The analogy between magnons and phonons is established. Then, the exact 1- and 2-magnon spectra of ferromagnets are obtained, with bound states and scattering states being analyzed separately. The many-magnon states are obtained in a low-density approximation, and the effects of surfaces assessed.
In antiferromagnetism, the XY and XYZ (Heisenberg) antiferro-magnets are solved exactly in one dimension by means of Bethe’s ansatz.
Finally, the topological excitationk known as “solitons” are introduced, their nonlinear equations of motion are solved exactly, and various properties derived semi-rigorously.
KeywordsGround State Energy Spin Wave Heisenberg Model Elementary Excitation Bound State Energy
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