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Symmetry, Integrability and Geometry: Methods and Applications, 2015, Volume 11, 062, 18 pp.
DOI: https://doi.org/10.3842/SIGMA.2015.062
(Mi sigma1043)
 

Topological Monodromy of an Integrable Heisenberg Spin Chain

Jeremy Lane

Department of Mathematics, University of Toronto, 40 St. George Street, Toronto, Ontario, Canada M5S 2E4
References:
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.
Keywords: integrable system; monodromy; Lagrangian fibration; Heisenberg spin chain.
Received: November 27, 2014; in final form July 29, 2015; Published online July 31, 2015
Bibliographic databases:
Document Type: Article
MSC: 37J35; 53D12
Language: English
Citation: Jeremy Lane, “Topological Monodromy of an Integrable Heisenberg Spin Chain”, SIGMA, 11 (2015), 062, 18 pp.
Citation in format AMSBIB
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