Gaudin models with ${\CU}_q(\mathfrak{osp}(1 | 2))$ symmetry

TL;DR

This paper introduces an exact solution to a Gaudin model with ${ m U}_q( ext{osp}(1|2))$ symmetry, utilizing coalgebra supersymmetry to diagonalize commuting observables.

Contribution

It provides the first exact solution for a Gaudin model based on the q-deformed superalgebra ${ m U}_q( ext{osp}(1|2))$, highlighting the role of coalgebra supersymmetry.

Findings

Exact eigenvectors and eigenvalues obtained

Complete set of commuting observables diagonalized

Solution based on coalgebra supersymmetry

Abstract

We consider a Gaudin model related to the q-deformed superalgebra ${\CU}_q(\mathfrak{osp}(1 | 2))$. We present an exact solution to that system diagonalizing a complete set of commuting observables, and providing the corresponding eigenvectors and eigenvalues. The approach used in this paper is based on the coalgebra supersymmetry of the model.