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Introduction to the nested algebraic Bethe ansatz

by N. A. Slavnov

Submission summary

As Contributors: Nikita Slavnov
Arxiv Link: (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


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:
Editor-in-charge assigned

Author comments upon resubmission

We changed the text according to the referee's comments.

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

Reports on this Submission

Anonymous Report 1 on 2020-8-4 Invited Report


Excellent lecture notes on the Nested Algebraic Bethe Ansatz.




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.

  • validity: -
  • significance: -
  • originality: -
  • clarity: -
  • formatting: -
  • grammar: -

Anonymous Report 2 on 2020-8-4 Invited Report


As in my previous report


No weaknesses


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

  • validity: high
  • significance: high
  • originality: top
  • clarity: high
  • formatting: excellent
  • grammar: good

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