# 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} }

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…

## 12 Citations

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, MathematicsJournal 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, MathematicsSciPost 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, MathematicsJournal 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, MathematicsJournal 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, MathematicsAnnales 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, MathematicsJournal 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…