Form factors in<i>S</i><i>U</i>(3)-invariant integrable models

Belliard, S.; Pakuliak, S.; Ragoucy, É.; Slavnov, N. A.

doi:10.1088/1742-5468/2013/04/p04033

Cited by 58 publications

(91 citation statements)

References 33 publications

(69 reference statements)

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“…Let us denote by δ (i) b (λ) the polynomials defined in the previous section just making explicit that we have fixed δ 0 = k i for some fixed i ∈ {1, ..., n}. Moreover, let us define the following N × N operator matrix of elements: 33) and the rank one central matrix:…”

Section: Q-operator Reconstruction By Sovmentioning

confidence: 99%

Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables

Maillet

Niccoli

2019

SciPost Phys.

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In this paper we apply our new separation of variables approach to completely characterize the transfer matrix spectrum for quantum integrable lattice models associated to fundamental evaluation representations of U q ( gl n ) with general quasi-periodic boundary conditions. We consider here the case of generic deformations associated to a parameter q which is not a root of unity. The Separation of Variables (SoV) basis for the transfer matrix spectral problem is generated by using the action of the transfer matrix itself on a generic covector of the Hilbert space, following the general procedure described in our paper [1]. Such a SoV construction allows to prove that for general values of the parameters defining the model the transfer matrix is diagonalizable and with simple spectrum for any twist matrix which is also diagonalizable with simple spectrum. Then, using together the knowledge of such a SoV basis and of the fusion relations satisfied by the hierarchy of transfer matrices, we derive a complete characterization of the transfer matrix eigenvalues and eigenvectors as solutions of a system of polynomial equations of order n + 1. Moreover, we show that such a SoV discrete spectrum characterization is equivalently reformulated in terms of a finite difference functional equation, the quantum spectral curve equation, under a proper choice of the set of its solutions. A construction of the associated Q-operator induced by our SoV approach is also presented.

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Section: Q-operator Reconstruction By Sovmentioning

confidence: 99%

Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables

Maillet

Niccoli

2019

SciPost Phys.

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“…There, an analog of IzerginKorepin formula for the scalar product of generic off-shell Bethe vectors and a determinant representation for the norm of the on-shell vectors were found. Recently various particular cases of scalar products were studied in [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

The algebraic Bethe ansatz for scalar products inSU(3)-invariant integrable models

Belliard¹,

Pakuliak²,

Ragoucy³

et al. 2012

J. Stat. Mech.

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137

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“…In the case of super-Yangians Y (gl 2|1 ) and Y (gl 1|2 ), a determinant representation was found for arbitrary diagonal twist matrix M = diag{κ 1 , κ 2 , κ 3 } [38]. In the case of the Yangian Y (gl 3 ) and a twist matrix M = diag{κ 1 , κ 2 , κ 3 }, a determinant formula for the scalar product was found up to corrections in (κ i − 1)(κ j − 1) [39].…”

Section: Determinant Formulamentioning

confidence: 97%

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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Form factors inSU(3)-invariant integrable models

Cited by 58 publications

References 33 publications

Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables

Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables

The algebraic Bethe ansatz for scalar products inSU(3)-invariant integrable models

Nested Algebraic Bethe Ansatz in integrable models: recent results

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