Nonlinear dynamics of the classical isotropic Heisenberg antiferromagnetic chain: The sigma model sector and the kink sector |
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| Affiliation: | 1. Nizhny Novgorod State Technical University n.a. R.E. Alekseev, Nizhny Novgorod 603950, Russia;2. Institute for Physics of Microstructures, Russian Academy of Sciences, Nizhny Novgorod 603950, Russia;3. N.I. Lobachevsky State University of Nizhny Novgorod, Nizhny Novgorod 603950, Russia;1. ENEA – Centro Ricerche Frascati, Via Enrico Fermi 45, 00044 Frascati, Rome, Italy;2. University of Palermo, Department of Mathematics, Via Archirafi, 34, 90123 Palermo, Italy |
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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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