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Introduction to the nested algebraic Bethe ansatz
by N. A. Slavnov
This Submission thread is now published as
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: | 2020-08-26 |
| Date submitted: | 2020-07-31 18:29 |
| Submitted by: | Slavnov, Nikita |
| Submitted to: | SciPost Physics Lecture Notes |
| Ontological classification | |
|---|---|
| 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)
Reports on this Submission
Report
For the revised version the author has carefully edited his manuscript following the suggestions of the four referees. This further improved the quality. In particular, he has added more explanatory text at the beginning of each section which makes the lecture notes more accessible to learners.
Strengths
Excellent lecture notes on the Nested Algebraic Bethe Ansatz.
Weaknesses
None
Report
The manuscript was considerably improved by the author. The most essential suggestions from my previous report are taken into account. I specially appreciated the brief explanations in the beginning of each section. I think that these excellent lecture notes are perfectly suitable for publication in the Les Houches volume in its present form.