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Introduction to the nested algebraic Bethe ansatz
by N. A. Slavnov
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Submission summary
| Authors (as registered SciPost users): | Nikita Slavnov |
| Submission information | |
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| Preprint Link: | https://arxiv.org/abs/1911.12811v2 (pdf) |
| Date accepted: | Aug. 26, 2020 |
| Date submitted: | July 31, 2020, 6:29 p.m. |
| Submitted by: | Slavnov, Nikita |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
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| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions and explicit formulas for the Bethe vectors. We also give a representation for the Bethe vectors in the form of a trace formula.
Author comments upon resubmission
List of changes
We extend description of the application of the nested algebraic Bethe ansatz in physics.
We explain how off-shell Bethe vectors appear in calculations of matrix elements of local operators.
We give the explicit solution of the quantum inverse problem.
We mention a method to construct Bethe vectors via Sklyanin's B-operator.
The content of two appendices is moved to the main text.
The list of references is extended.
Typos are corrected
Published as SciPost Phys. Lect. Notes 19 (2020)
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