Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries
High Energy Physics - Theory
2023-12-11 v2 Mathematical Physics
math.MP
Abstract
We study the Hilbert space of the Class 5 model described in arXiv:1904.12005. Despite being integrable, neither its transfer matrix nor its Hamiltonian are diagonalisable, meaning that the usual Algebraic Bethe Ansatz does not provide the full Hilbert space. Instead, we make use of the symmetries of the model to construct the Jordan blocks of the transfer matrix. We also show that the Hamiltonian and the transfer matrix, despite commuting, do not have the same Jordan block structure.
Keywords
Cite
@article{arxiv.2309.10044,
title = {Jordan blocks and the Bethe ansatz III: Class 5 model and its symmetries},
author = {Juan Miguel Nieto García},
journal= {arXiv preprint arXiv:2309.10044},
year = {2023}
}
Comments
20 pages; v2 significant changes in section 4 and appendix A