Symmetry, Integrability and Geometry: Methods and Applications, 2017
Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe an... more Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors in the composite models with supersymmetry based on the super-Yangians Y [gl(2|1)] and Y [gl(1|2)] are derived.
The integrable close and open chain models can be formulated in terms of generators of the Hecke ... more The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is consedered. Finally, we discuss some questions relating to the general open Hecke chain models.
The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra... more The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.
ABSTRACT The paper deals with the tensor product decomposition problem. Tensor product decomposit... more ABSTRACT The paper deals with the tensor product decomposition problem. Tensor product decompositions are of great importance in the quantum physics. A short outline of the state of the art for the of semisimple Lie groups is mentioned. The generality of generating functions is used to solve tensor products. The corresponding generating function is rational. The feature of this technique lies in the fact that the decompositions of all tensor products of all irreducible representations are solved simultaneously. Obtaining the generating function is a difficult task in general. We propose some changes to an algorithm using Patera-Sharp character generators to find this generating function, which simplifies the whole problem to simple operations over rational functions.
Symmetry, Integrability and Geometry: Methods and Applications, 2017
Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe an... more Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors in the composite models with supersymmetry based on the super-Yangians Y [gl(2|1)] and Y [gl(1|2)] are derived.
The integrable close and open chain models can be formulated in terms of generators of the Hecke ... more The integrable close and open chain models can be formulated in terms of generators of the Hecke algebras. In this review paper, we describe in detail the Bethe ansatz for the XXX and the XXZ integrable close chain models. We find the Bethe vectors for two-component and inhomogeneous models. We also find the Bethe vectors for the fermionic realization of the integrable XXX and XXZ close chain models by means of the algebraic and coordinate Bethe ansatz. Special modification of the XXZ closed spin chain model ("small polaron model") is consedered. Finally, we discuss some questions relating to the general open Hecke chain models.
The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra... more The paper deals with algebraic Bethe ansatz for XXX-spin chain. Generators of Yang-Baxter algebra are expressed in basis of free fermions and used to calculate explicit form of Bethe vectors. Their relation to N-component models is used to prove conjecture about their form in general. Some remarks on inhomogeneous XXX-spin chain are included.
ABSTRACT The paper deals with the tensor product decomposition problem. Tensor product decomposit... more ABSTRACT The paper deals with the tensor product decomposition problem. Tensor product decompositions are of great importance in the quantum physics. A short outline of the state of the art for the of semisimple Lie groups is mentioned. The generality of generating functions is used to solve tensor products. The corresponding generating function is rational. The feature of this technique lies in the fact that the decompositions of all tensor products of all irreducible representations are solved simultaneously. Obtaining the generating function is a difficult task in general. We propose some changes to an algorithm using Patera-Sharp character generators to find this generating function, which simplifies the whole problem to simple operations over rational functions.
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