# Nested Algebraic Bethe Ansatz in integrable models: recent results

@article{Pakuliak2018NestedAB,
title={Nested Algebraic Bethe Ansatz in integrable models: recent results},
author={Stanislav Z. Pakuliak and Eric Ragoucy and Nikita Andreevich Slavnov},
journal={SciPost Physics Lecture Notes},
year={2018}
}
• Published 28 February 2018
• Physics, Mathematics
• SciPost Physics Lecture Notes
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…
Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
• Mathematics, Physics
• 2019
We present a nested algebraic Bethe ansatz for one-dimensional open so(2n)- and sp(2n)-symmetric spin chains with diagonal boundary conditions and described by the extended twisted Yangian. We use a
Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains
• Physics, Mathematics
• 2020
Abstract We construct exact eigenvectors and eigenvalues for U q ( sp 2 n ) - and U q ( so 2 n ) -symmetric closed spin chains by means of a nested algebraic Bethe ansatz method. We use a fusion
Separation of variables bases for integrable glM|N and Hubbard models
• 2019
We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous glM|N supersymmetric integrable models and for the inhomogeneous Hubbard model both defined with
On scalar products and form factors by separation of variables: the antiperiodic XXZ model
• Physics, Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2021
We consider the XXZ spin-1/2 Heisenberg chain with antiperiodic boundary conditions. The inhomogeneous version of this model can be solved by separation of variables, and the eigenstates can be
Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
• Physics, Mathematics
SciPost Physics
• 2019
We apply our new approach of quantum Separation of Variables (SoV) to the complete characterization of the transfer matrix spectrum of quantum integrable lattice models associated to
Separation of variables bases for integrable $gl_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
• Physics, Mathematics
• 2019
We construct quantum Separation of Variables (SoV) bases for both the fundamental inhomogeneous $gl_{\mathcal{M}|\mathcal{N}}$ supersymmetric integrable models and for the inhomogeneous Hubbard model
Complete spectrum of quantum integrable lattice models associated to $\boldsymbol {\mathcal{U}_{q} (\widehat{gl_{n}})}$ by separation of variables
• Physics, Mathematics
Journal of Physics A: Mathematical and Theoretical
• 2019
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
New compact construction of eigenstates for supersymmetric spin chains
• Physics, Mathematics
Journal of High Energy Physics
• 2018
A bstractThe problem of separation of variables (SoV) in supersymmetric spin chains is closely related to the calculation of correlation functions in N=4$$\mathcal{N}=4$$ SYM theory which is
Nested Algebraic Bethe Ansatz for Open Spin Chains with Even Twisted Yangian Symmetry
• Physics, Mathematics
Annales Henri Poincaré
• 2018
We present a nested algebraic Bethe ansatz for a one-dimensional open spin chain whose boundary quantum spaces are irreducible $$\mathfrak {so}_{2n}$$so2n- or \mathfrak
Correlation functions and transport coefficients in generalised hydrodynamics
• Physics, Mathematics
Journal of Statistical Mechanics: Theory and Experiment
• 2022
We review the recent advances on exact results for dynamical correlation functions at large scales and related transport coefficients in interacting integrable models. We discuss Drude weights,

## References

SHOWING 1-10 OF 80 REFERENCES
Form factors of local operators in the algebraic Bethe ansatz
• Mathematics
• 2015
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the total monodromy matrix of the model is
Zero modes method and form factors in quantum integrable models
• Physics, Mathematics
• 2015
Abstract We study integrable models solvable by the nested algebraic Bethe ansatz and possessing GL ( 3 ) -invariant R-matrix. Assuming that the monodromy matrix of the model can be expanded into
Scalar products of Bethe vectors in models with gl(2|1) symmetry 1. Super-analog of Reshetikhin formula
• Physics
• 2016
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(2|1)$ symmetry. Using explicit formulas of the monodromy matrix
GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
• Mathematics, Physics
• 2015
We study integrable models solvable by the nested algebraic Bethe ansatz and possessing the GL(3)-invariant R-matrix. We consider a composite model where the to- tal monodromy matrix of the model is
Form factors of local operators in supersymmetric quantum integrable models
• Mathematics, Physics
• 2017
We apply the nested algebraic Bethe ansatz to the models with gl(2|1) and gl}(1|2) supersymmetry. We show that form factors of local operators in these models can be expressed in terms of the
Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
• Physics, Mathematics
• 2016
Abstract We study integrable models solvable by the nested algebraic Bethe ansatz and described by gl ( 2 | 1 ) or gl ( 1 | 2 ) superalgebras. We obtain explicit determinant representations for form
Bethe Ansatz and Bethe Vectors Scalar Products
• Mathematics, Physics
• 2010
An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_3)$ is given. This
GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
• Mathematics, Physics
• 2015
We consider a composite generalized quantum integrable model solvable by the nested algebraic Bethe ansatz. Using explicit formulas of the action of the monodromy matrix elements onto Bethe vectors
Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 1. Super-analog of Reshetikhin formula
• Mathematics, Physics
• 2016
We study scalar products of Bethe vectors in integrable models solvable by nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(2|1)$ symmetry. Using explicit formulas of the monodromy matrix
Scalar products of Bethe vectors in models with gl(2|1) symmetry 2. Determinant representation
• Mathematics, Physics
• 2016
We study integrable models with $\mathfrak{gl}(2|1)$ symmetry and solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for scalar products of Bethe vectors, when the