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… Expand
Nested algebraic Bethe ansatz for orthogonal and symplectic open spin chains
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 aExpand
Nested algebraic Bethe ansatz for deformed orthogonal and symplectic spin chains
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 fusionExpand
Separation of variables bases for integrable glM|N and Hubbard models
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 withExpand
On scalar products and form factors by Separation of Variables: the antiperiodic XXZ model
  • H. Pei, V. Terras
  • 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 (SoV), and the eigenstates canExpand
Complete spectrum of quantum integrable lattice models associated to Y(gl(n)) by separation of variables
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 toExpand
Separation of variables bases for integrable $gl_{\mathcal{M}|\mathcal{N}}$ and Hubbard models
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 modelExpand
Complete spectrum of quantum integrable lattice models associated to $\boldsymbol {\mathcal{U}_{q} (\widehat{gl_{n}})}$ by separation of variables
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 evaluationExpand
New compact construction of eigenstates for supersymmetric spin chains
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 isExpand
Nested Algebraic Bethe Ansatz for Open Spin Chains with Even Twisted Yangian Symmetry
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 $$\mathfrakExpand
Effective free-fermionic form factors and the XY spin chain
We introduce effective form factors for one-dimensional lattice fermions with arbitrary phase shifts. We study tau functions defined as series of these form factors. On the one hand we perform theExpand
...
1
2
...

References

SHOWING 1-10 OF 80 REFERENCES
Form factors of local operators in the algebraic Bethe ansatz
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 isExpand
Zero modes method and form factors in quantum integrable models
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 intoExpand
Scalar products of Bethe vectors in models with gl(2|1) symmetry 1. Super-analog of Reshetikhin formula
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 matrixExpand
GL(3)-Based Quantum Integrable Composite Models. II. Form Factors of Local Operators
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 isExpand
Form factors of local operators in supersymmetric quantum integrable models
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 theExpand
Form factors of the monodromy matrix entries in gl(2|1)-invariant integrable models
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 formExpand
Bethe Ansatz and Bethe Vectors Scalar Products
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. ThisExpand
GL(3)-Based Quantum Integrable Composite Models. I. Bethe Vectors
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 vectorsExpand
Scalar products of Bethe vectors in models with $\mathfrak{gl}(2|1)$ symmetry 1. Super-analog of Reshetikhin formula
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 matrixExpand
Scalar products of Bethe vectors in models with gl(2|1) symmetry 2. Determinant representation
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 theExpand
...
1
2
3
4
5
...