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Advances in Condensed Matter Physics
Volume 2015, Article ID 954524, 3 pages
Research Article

New Topological Configurations in the Continuous Heisenberg Spin Chain: Lower Bound for the Energy

Laboratoire de Physique Théorique et Modélisation, Université de Cergy-Pontoise, 95302 Cergy-Pontoise, France

Received 19 April 2015; Accepted 12 August 2015

Academic Editor: Oleg Derzhko

Copyright © 2015 Rossen Dandoloff. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


In order to study the spin configurations of the classical one-dimensional Heisenberg model, we map the normalized unit vector, representing the spin, on a space curve. We show that the total chirality of the configuration is a conserved quantity. If, for example, one end of the space curve is rotated by an angle of 2π relative to the other, the Frenet frame traces out a noncontractible loop in and this defines a new class of topological spin configurations for the Heisenberg model.