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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 accepted: 2020-08-26
Date submitted: 2020-07-31 18:29
Submitted by: Slavnov, Nikita
Submitted to: SciPost Physics Lecture Notes
Academic field: Physics
Specialties:
  • 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.

Ontology / Topics

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Bethe Ansatz

Published as SciPost Phys. Lect. Notes 19 (2020)



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 3 on 2020-8-18 Invited Report

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.

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

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.

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

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

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

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