Zobrazeno 1 - 10
of 132
pro vyhledávání: '"A. Liashyk"'
A new method is introduced to derive general recurrence relations for off-shell Bethe vectors in quantum integrable models with either type $\mathfrak{gl}_n$ or type $\mathfrak{o}_{2n+1}$ symmetries. These recurrence relations describe how to add a s
Externí odkaz:
http://arxiv.org/abs/2412.05224
Autor:
Liashyk, A., Pakuliak, S.
The connection between the R-matrix realization and Drinfeld's realization of the quantum loop algebra $U_q(D^{(2)}_n)$ is considered using the Gaussian decomposition approach proposed by J. Ding and I. B. Frenkel. Our main result is a description of
Externí odkaz:
http://arxiv.org/abs/2409.02021
In this paper, we develop the framework for quantum integrable systems on an integrable classical background. We call them hybrid quantum integrable systems (hybrid integrable systems), and we show that they occur naturally in the semiclassical limit
Externí odkaz:
http://arxiv.org/abs/2405.17865
Autor:
A. Liashyk, S. Z. Pakuliak
Publikováno v:
SciPost Physics, Vol 12, Iss 5, p 146 (2022)
We consider $\rm R$-matrix realization of the quantum deformations of the loop algebras $\tilde{\mathfrak{g}}$ corresponding to non-exceptional affine Lie algebras of type $\widehat{\mathfrak{g}}=A^{(1)}_{N-1}$, $B^{(1)}_n$, $C^{(1)}_n$, $D^{(1)}_
Externí odkaz:
https://doaj.org/article/8c3982d3ec5c4f29b69edc5118ce1cd0
Autor:
A. Liashyk, N. A. Slavnov
Publikováno v:
Journal of High Energy Physics, Vol 2018, Iss 6, Pp 1-32 (2018)
Abstract We consider quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl3 $$ \mathfrak{g}{\mathfrak{l}}_3 $$-invariant R-matrix. We study a new recently proposed approach to construct on-shell Bethe vectors of th
Externí odkaz:
https://doaj.org/article/e36f8dcc8892462bb4955fcbecd747d5
Publikováno v:
Nuclear Physics B, Vol 926, Iss C, Pp 256-278 (2018)
We study quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing gl(m|n)-invariant R-matrix. We compute the norm of the Hamiltonian eigenstates. Using the notion of a generalized model we show that the square of the nor
Externí odkaz:
https://doaj.org/article/2e1694f734a8409d87f19e889e1c34dc
Publikováno v:
Nuclear Physics B, Vol 923, Iss C, Pp 277-311 (2017)
We study scalar products of Bethe vectors in the models solvable by the nested algebraic Bethe ansatz and described by gl(m|n) superalgebra. Using coproduct properties of the Bethe vectors we obtain a sum formula for their scalar products. This formu
Externí odkaz:
https://doaj.org/article/a96fc89197b0462094ddacf77b6c8957
Publikováno v:
Nuclear Physics B, Vol 911, Iss C, Pp 902-927 (2016)
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 factors of the monodromy matrix entries. We show that all form factors
Externí odkaz:
https://doaj.org/article/6ad309ff7c8e4a7ebf1ce5cf09c8e0d3
Publikováno v:
Nuclear Physics B, Vol 903, Iss C, Pp 150-163 (2016)
We extend the quantum–classical duality to the trigonometric (hyperbolic) case. The duality establishes an explicit relationship between the classical N-body trigonometric Ruijsenaars–Schneider model and the inhomogeneous twisted XXZ spin chain o
Externí odkaz:
https://doaj.org/article/e127c731ebe9446493113963d6152385
Autor:
Liashyk, A., Pakuliak, S. Z.
Publikováno v:
J. Phys. A: Math. Theor. 2022 (55) 075201
The zero modes method is applied in order to get action of the monodromy matrix entries onto off-shell Bethe vectors in quantum integrable models associated with $U_q(\mathfrak{gl}_N)$-invariant $R$-matrices. The action formulas allow to get recurren
Externí odkaz:
http://arxiv.org/abs/2109.07528