SciPost Submission Page
Introduction to the nested algebraic Bethe ansatz
by N. A. Slavnov
Submission summary
| As Contributors: | Nikita Slavnov |
| Arxiv Link: | https://arxiv.org/abs/1911.12811v2 (pdf) |
| Date submitted: | 2020-07-31 18:29 |
| Submitted by: | Slavnov, Nikita |
| Submitted to: | SciPost Physics Lecture Notes |
| Discipline: | Physics |
| Subject area: | Mathematical Physics |
| 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.
Current status:
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
Submission & Refereeing History
You are currently on this page
Reports on this Submission
Anonymous Report 1 on 2020-8-4 Invited Report
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.
Anonymous Report 2 on 2020-8-4 Invited Report
Strengths
As in my previous report
Weaknesses
No weaknesses
Report
The author has implemented the remarks that I have suggested in my previous report. Thus, I suggest the publication of the manuscript in the current form.
Requested changes
no changes