Scalar products and norm of Bethe vectors for integrable models based on  $U_q(\widehat{\mathfrak{gl}}_{n})$

Hutsalyuk, A.; Liashyk, A.; Pakuliak, S.; Ragoucy, É.; Slavnov, N. A.

doi:10.21468/scipostphys.4.1.006

Cited by 17 publications

(54 citation statements)

References 98 publications

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“…• The representation of the norm of BVs are described in [42] for Y (gl n ) and Y (gl m|p ). Similar representations for U q ( gl n ) can be found in [21].…”

Section: Norm Of On-shell Bvs: Gaudin Determinantsupporting

confidence: 54%

Nested Algebraic Bethe Ansatz in integrable models: recent results

Pakuliak

Ragoucy

Slavnov

2018

SciPost Phys. Lect. Notes

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We review the recent results we have obtained in the framework of algebraic Bethe ansatz based on algebras and superalgebras of rank greater than 1 or on their quantum deformation. We present different expressions (explicit, recursive or using the current realization of the algebra) for the Bethe vectors. Then, we provide a general expression (as sum over partitions) for their scalar products. For some particular cases (in the case of gl(3)gl(3) or its quantum deformation, or of gl(2|1)gl(2|1)), we provide determinant expressions for the scalar products. We also compute the form factors of the monodromy matrix entries, and give some general methods to relate them. A coproduct formula for Bethe vectors allows to get the form factors of composite models.

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“…• The representation of the norm of BVs are described in [42] for Y (gl n ) and Y (gl m|p ). Similar representations for U q ( gl n ) can be found in [21].…”

Section: Norm Of On-shell Bvs: Gaudin Determinantsupporting

confidence: 54%

Nested Algebraic Bethe Ansatz in integrable models: recent results

Pakuliak

Ragoucy

Slavnov

2018

SciPost Phys. Lect. Notes

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“…For q-deformed algebra case U q ( gl n ), the highest coefficient Z q (x|t) was introduced in [29]. Its symmetric property formally coincides with (5.12):…”

Section: Resultsmentioning

confidence: 99%

New symmetries of $ {\mathfrak{gl}(N)}$ -invariant Bethe vectors

Liashyk¹,

Pakuliak²,

Ragoucy³

et al. 2019

J. Stat. Mech.

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We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(N )-invariant R-matrix. We study two types of Bethe vectors. The first type corresponds to the original monodromy matrix. The second type is associated to a monodromy matrix closely related to the inverse of the monodromy matrix. We show that these two types of the Bethe vectors are identical up to normalization and reshuffling of the Bethe parameters. To prove this correspondence we use the current approach. This identity gives new combinatorial relations for the scalar products of the Bethe vectors. The q-deformed case, as well as the superalgebra case, are also evoked in the conclusion. 1 a.

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“…In this section we adapt the method described in [37] and [38] to the present case. As the expressions appearing during the rest of this article usually involve several products, we will use the following shorthand notations when need to multiply over sets of rapidities…”

Section: The Composite Model Trickmentioning

confidence: 99%

“…Some examples of these efforts are given by [36]. Here we will be using the "composite model trick", developed in [37] for computing scalar products in models with U q (gl m ) symmetry, to compute off-shell scalar products in spin chains constructed using the R-matrices found in [21] and [24]. In the first case (pure R-R case)…”

mentioning

confidence: 99%

Norms and scalar products forAdS₃

García¹,

Торриелли²

2020

J. Phys. A: Math. Theor.

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We compute scalar products and norms of Bethe vectors in the massless sector of AdS3 integrable superstring theories, by exploiting the general difference form of the S-matrix of massless excitations in the pure Ramond-Ramond case, and the difference form valid only in the BMN limit in the mixedflux case. We obtain determinant-like formulas for the scalar products, generalising a procedure developed in previous literature for standard R-matrices to the present non-conventional situation.We verify our expressions against explicit calculations using Bethe vectors for chains of small length, and perform some computer tests of the exact formulas as far as numerical accuracy sustains us. This should be the first step towards the derivation of integrable form-factors and correlation functions for the AdS3 S-matrix theory.

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Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_{n})$

Cited by 17 publications

References 98 publications

Nested Algebraic Bethe Ansatz in integrable models: recent results

Nested Algebraic Bethe Ansatz in integrable models: recent results

New symmetries of $ {\mathfrak{gl}(N)}$ -invariant Bethe vectors

Norms and scalar products forAdS₃

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Scalar products and norm of Bethe vectors for integrable models based on $U_q(\widehat{\mathfrak{gl}}_{n})$

Cited by 17 publications

References 98 publications

Nested Algebraic Bethe Ansatz in integrable models: recent results

Nested Algebraic Bethe Ansatz in integrable models: recent results

New symmetries of $ {\mathfrak{gl}(N)}$ -invariant Bethe vectors

Norms and scalar products forAdS3

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Norms and scalar products forAdS₃