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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
Submission summary
| Authors (as registered SciPost users): | Eric Ragoucy |
| Submission information | |
|---|---|
| Preprint Link: | https://arxiv.org/abs/2503.01578v2 (pdf) |
| Date submitted: | May 14, 2025, 9:53 a.m. |
| Submitted by: | Ragoucy, Eric |
| Submitted to: | SciPost Physics |
| Ontological classification | |
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| 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.
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- 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
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.
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