Soft modes in the one-dimensional Heisenberg antiferromagnet near saturation

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Abstract
The elementary excitations of the one-dimensional spin-S Heisenberg antiferromagnet near saturation are explained, with special attention to the soft mode, in terms of a gas of interacting magnons. Recent numerical studies of the antiferromagnet in a magnetic field uncovered the presence of the soft mode at a magnetization-dependent wave number for large magnetizations. We show that very near saturation and for large spins the antiferromagnet can be written in terms of a gas of magnons interacting via repulsive δ-function potentials, a system with a known Bethe-ansatz solution. The soft mode can then be explained as a Kohn-anomaly-type excitation above a quasi-Fermi-sea. Other elementary excitations form a particle-hole-type double continuum. The soft mode’s apparent physical observability is indicated by a shoulder at the appropriate wave number in the integrated longitudinal intensity.