On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetry
Abstract
We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with -symmetry for any simple Lie algebra . Starting the nesting process by removing a single simple root from , we use the residual charge and the block Gauss decomposition of the -matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and the AB commutation relation.
Keywords
Cite
@article{arxiv.2405.20177,
title = {On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetry},
author = {Allan John Gerrard},
journal= {arXiv preprint arXiv:2405.20177},
year = {2024}
}
Comments
- Corrected the statement of Conjecture 6.3, as the order of the tensor product was inconsistent; this correction has been applied throughout. - Added two example calculations after Conjecture 6.3. - Added a table detailing the nesting of Yangian representations for a number of fundamental representations. - Fixed some typos and corrected a broken reference