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

摘要

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 2πrelative to the other, the Frenet frame traces out a noncontractible loop inSO(3)and this defines a new class of topological spin configurations for the Heisenberg model.