On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetry
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2024
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| _version_ | 1866916282975125504 |
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| author | Gerrard, Allan John |
| author_facet | Gerrard, Allan John |
| contents | We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from $\mathfrak{g}$, we use the residual $U(1)$ charge and the block Gauss decomposition of the $R$-matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and the AB commutation relation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_20177 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetry Gerrard, Allan John Mathematical Physics High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from $\mathfrak{g}$, we use the residual $U(1)$ charge and the block Gauss decomposition of the $R$-matrix to derive many standard results in the Bethe ansatz, such as the nesting of Yangian algebras, and the AB commutation relation. |
| title | On the nested algebraic Bethe ansatz for spin chains with simple $\mathfrak{g}$-symmetry |
| topic | Mathematical Physics High Energy Physics - Theory Quantum Algebra Exactly Solvable and Integrable Systems |
| url | https://arxiv.org/abs/2405.20177 |