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Scalar products and norm of Bethe vectors in $\mathfrak{o}_{2n+1}$ invariant integrable models
by A. Liashyk, S. Pakuliak, E. Ragoucy
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Submission summary
| Authors (as registered SciPost users): | Eric Ragoucy |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.01578v2 (pdf) |
| Date accepted: | June 30, 2025 |
| Date submitted: | May 14, 2025, 9:53 a.m. |
| Submitted by: | Eric Ragoucy |
| Submitted to: | SciPost Physics |
| Ontological classification | |
|---|---|
| Academic field: | Physics |
| Specialties: |
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| Approach: | Theoretical |
Abstract
We compute scalar products of off-shell Bethe vectors in models with $o_{2n+1}$ symmetry. The scalar products are expressed as a sum over partitions of the Bethe parameter sets, the building blocks being the so-called highest coefficients. We prove some recurrence relations and a residue theorem for these highest coefficients, and prove that they are consistent with the reduction to $gl_n$ invariant models. We also express the norm of on-shell Bethe vectors as a Gaudin determinant.
Author indications on fulfilling journal expectations
- Provide a novel and synergetic link between different research areas.
- Open a new pathway in an existing or a new research direction, with clear potential for multi-pronged follow-up work
- Detail a groundbreaking theoretical/experimental/computational discovery
- Present a breakthrough on a previously-identified and long-standing research stumbling block
Author comments upon resubmission
We thanks the referees for their valuable reports. According to their requests and remarks, we have expanded the introduction, both for the general context, and also for the specific o(n) models, adding several references.
Still in the introduction, we also clarified the notion of off-shell Bethe vectors. They are the objects for which we compute the scalar products,
which play a role in the entanglement.
Finally, we summarized the different results we present in the paper.
We also added a conclusion, detailing the possible generalizations of our work, as well as its possible applications.
Apart from the correction to the typos noted by the referees, we made the changes described below
Still in the introduction, we also clarified the notion of off-shell Bethe vectors. They are the objects for which we compute the scalar products,
which play a role in the entanglement.
Finally, we summarized the different results we present in the paper.
We also added a conclusion, detailing the possible generalizations of our work, as well as its possible applications.
Apart from the correction to the typos noted by the referees, we made the changes described below
List of changes
- We detailed the transposition anti-morphism between eqs (2.3) and (2.4)
- The functions $\lambda_i(z)$ are indeed not all free, we modified the sentences before eq (2.9) and before the paragraph 'Notation'
- We clarified the constraints on the polynomials entering eq (2.12)
- We detailed the connexion between the vacuum state, its dual, and their relation through the transposition, between eqs (2.16) and (2.17)
- We modified the sentence before eq (3.2), to encompass partitions in more than two subsets
- At the beginning of section 5.2, we explained how the reduction to gl(n) model occurs
- At the beginning of section 7 we quoted Gaudin's work.
- We added an acknowledgement section.
Published as SciPost Phys. 19, 023 (2025)
Reports on this Submission
Report
Dear Editor,
I think that the Authors have improved their manuscript and that they have implemented the majority of the issues that I have pointed out in my first report. In particular, they have improved their introduction and also written a conclusion where were single out some interesting future directions of research that are now open thanks to their research. They have modified the intro to section 5.2 in this way answering to my main requirements of clarifications of point a) of my report.
I recommend so that the paper is published on SciPost after proofreading, e.g. I have found in the line 2 of page 3 a misprint after “see proposition 6.1 and” there should be “its” and not “is”.
I think that the Authors have improved their manuscript and that they have implemented the majority of the issues that I have pointed out in my first report. In particular, they have improved their introduction and also written a conclusion where were single out some interesting future directions of research that are now open thanks to their research. They have modified the intro to section 5.2 in this way answering to my main requirements of clarifications of point a) of my report.
I recommend so that the paper is published on SciPost after proofreading, e.g. I have found in the line 2 of page 3 a misprint after “see proposition 6.1 and” there should be “its” and not “is”.
Recommendation
Publish (surpasses expectations and criteria for this Journal; among top 10%)
Report
The authors have addressed all issues raised by the referees in a serious manner and have thoroughly revised their manuscript. I to not see any further obstacle for an immediate publication.
Recommendation
Publish (easily meets expectations and criteria for this Journal; among top 50%)