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arXiv · 1411.7063

Topological Monodromy of an Integrable Heisenberg Spin Chain

Jeremy Lane
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Abstract

We investigate topological properties of a completely integrable system on $S^2\times S^2 \times S^2$ which was recently shown to have a Lagrangian fiber diffeomorphic to $\mathbb{R} P^3$ not displaceable by a Hamiltonian isotopy [Oakley J., Ph.D. Thesis, University of Georgia, 2014]. This system can be viewed as integrating the determinant, or alternatively, as integrating a classical Heisenberg spin chain. We show that the system has non-trivial topological monodromy and relate this to the geometric interpretation of its integrals.

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Jeremy Lane. 2015-07-31. Topological Monodromy of an Integrable Heisenberg Spin Chain. https://doi.org/10.3842/sigma.2015.062

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