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arXiv:math-ph/0310003

Exact solution of a supersymmetric Gaudin model

Julia Breiderhoff, Musso, Fabio, O. Ragnisco

Published Oct 3, 2003• 1 citation
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Abstract

A special case of the Gaudin model related to the superalgebra $osp(1,2)$ is investigated. An exact solution for the model in the spin-1/2 representation is presented. A complete set of commuting observables is diagonalized and the corresponding eigenvectors and eigenvalues are explicitly calculated. The approach used in this paper is based on the co-algebra symmetry of the model, already known from the spin-1/2 Calogero-Gaudin system.

DOI
10.48550/arxiv.math-ph/0310003

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Gaudin model based on the orthosymplectic Lie superalgebra osp(1|2) is studied. The eigenvectors of the osp(1|2) invariant Gaudin hamiltonians are constructed by algebraic Bethe Ansatz. Corresponding creation operators are defined by a recurrence relation. Furthermore, explicit solution to this recurrence relation is found. The action of the creation operators on the lowest spin vector yields Bethe vectors of the model. The relation between the Bethe vectors and solutions to the Knizhnik-Zamolodchikov equation of the corresponding super-conformal field theory is established. 1