Topological Monodromy of an Integrable Heisenberg Spin Chain

Symmetry Integrability and Geometry-Methods and Applications

article

Jeremy Lane¹ 

[1] Department of Mathematics, University of Toronto

关键词: integrable system;    monodromy;    Lagrangian fibration;    Heisenberg spin chain;   

DOI  :  10.3842/SIGMA.2015.062

来源: National Academy of Science of Ukraine

【 摘 要 】

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.

【 授权许可】

Unknown