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On completeness of Bethe Ansatz solutions for sl(2) Richardson–Gaudin systems

In: Physical and Mathematical Aspects of Symmetries

Author

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  • Jon Links

    (The University of Queensland, School of Mathematics and Physics)

Abstract

The Bethe Ansatz solution for the class of rational, sl(2) Richardson– Gaudin systems is presented. Completeness of this solution is discussed for the case where all operators are realised in terms of the spin-1/2 representation. This discussion is based on a set of operator identities. Next, a generalised system with broken u(1)-symmetry is introduced, which admits an analogous set of operator identities. Analysis of this generalised system shows that the Bethe Ansatz solution for it is also complete. The prospects for extending this approach to higher spin systems are mentioned.

Suggested Citation

  • Jon Links, 2017. "On completeness of Bethe Ansatz solutions for sl(2) Richardson–Gaudin systems," Springer Books, in: Sergio Duarte & Jean-Pierre Gazeau & Sofiane Faci & Tobias Micklitz & Ricardo Scherer & Francesco To (ed.), Physical and Mathematical Aspects of Symmetries, pages 239-244, Springer.
    • Handle: RePEc:spr:sprchp:978-3-319-69164-0_36
    DOI: 10.1007/978-3-319-69164-0_36
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