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Nonlinear dynamics of the classical isotropic Heisenberg antiferromagnetic chain: the sigma model sector and the kink sector

Radha Balakrishnan·Rossen Dandoloff
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Abstract

We identify two distinct low-energy sectors in the classical isotropic antiferromagnetic Heisenberg spin-S chain. In the continuum limit, we show that two types of rotation generators arise for the field in each sector. Using these, the Lagrangian for sector I is shown to be that of the nonlinear sigma model. Sector II has a null Lagrangian; Its Hamiltonian density is just the Pontryagin term. Exact solutions are found in the form of magnons and precessing pulses in I and moving kinks in II. The kink has `spin' S. Sector I has a higher minimum energy than II.

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Radha Balakrishnan, Rossen Dandoloff. 2001-04-05. Nonlinear dynamics of the classical isotropic Heisenberg antiferromagnetic chain: the sigma model sector and the kink sector. https://doi.org/10.1016/s0375-9601(02)01266-5

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