On zero-remainder conditions in the Bethe ansatz

Etienne Granet (1, 2) , Jesper Lykke Jacobsen (1, 3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 LPENS - Laboratoire de physique de l'ENS - ENS Paris
3 Champs Aléatoires et Systèmes hors d'Équilibre

We prove that physical solutions to the Heisenberg spin chain Bethe ansatz equations are exactly obtained by imposing two zero-remainder conditions. This bridges the gap between different criteria, yielding an alternative proof of a recently devised algorithm based on QQ relations, and solving its minimality issue.

Mots clés: Bethe Ansatz; Lattice Integrable Models; spin: chain; Bethe ansatz; Heisenberg; gap

Domaines: Physique des Hautes Energies - Théorie [hep-th]; Physique mathématique [math-ph]; Physique Générale [physics.gen-ph]

Etienne Granet, Jesper Lykke Jacobsen. On zero-remainder conditions in the Bethe ansatz. Journal of High Energy Physics, 2020, 03, pp.178. ⟨10.1007/JHEP03(2020)178⟩. ⟨hal-02350381⟩