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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2017 Springer International Publishing AG
About this paper
Cite this paper
Links, J. (2017). On completeness of Bethe Ansatz solutions for sl(2) Richardson–Gaudin systems. In: Duarte, S., Gazeau, JP., Faci, S., Micklitz, T., Scherer, R., Toppan, F. (eds) Physical and Mathematical Aspects of Symmetries. Springer, Cham. https://doi.org/10.1007/978-3-319-69164-0_36
Download citation
DOI: https://doi.org/10.1007/978-3-319-69164-0_36
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-69163-3
Online ISBN: 978-3-319-69164-0
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)