Hidden topological structure in the continuous Heisenberg spin chain

TL;DR

This paper introduces a novel topological classification of spin configurations in the 1D Heisenberg model by mapping spins to space curves and identifying conserved chirality, revealing knot-like structures.

Contribution

It proposes a new topological framework for analyzing spin configurations in the classical Heisenberg chain, highlighting the role of chirality and knot formation.

Findings

Total chirality is conserved in the model.

Knot-like configurations define a new topological class.

Space curve mapping reveals hidden topological structures.

Abstract

In order to study the spin configurations of the classical one-dimensional Heisenberg model, we map the normalized unit vector, representing the spin, to a space curve. We show that the total chirality of the configuration is a conserved quantity. When the space curve forms a knot, this defines a new class of topological spin configurations for the Heisenberg model.