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We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…

Mathematical Physics · Physics 2015-05-20 Rouven Frassek , Tomasz Lukowski , Carlo Meneghelli , Matthias Staudacher

We consider the N-site U_{q}(gl(N)) integrable spin chain with periodic and open diagonal soliton-preserving boundary conditions. By employing analytical Bethe ansatz techniques we are able to determine the spectrum and the corresponding…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy

We present the analytical Bethe ansatz for spin chains based on the superalgebras gl(M|N), $M\neq N$, with at each site an arbitrary representation (and including inhomogeneities). The calculation is done for closed and open spin chains. In…

High Energy Physics - Theory · Physics 2015-09-18 E. Ragoucy , G. Satta

We consider open XXX spins chain with two general boundary matrices submitted to one constraint, which is equivalent to the possibility to put the two matrices in a triangular form. We construct Bethe vectors from a generalized algebraic…

Mathematical Physics · Physics 2015-06-11 S. Belliard , N. Crampe , E. Ragoucy

A non homogeneous spin chain in the representations $ \{3 \}$ and $ \{3^*\}$ of $A_2$ is analyzed. We find that the naive nested Bethe ansatz is not applicable to this case. A method inspired in the nested Bethe ansatz, that can be applied…

High Energy Physics - Theory · Physics 2009-10-30 Julio Abad , Miguel Rios

The full set of polynomial solutions of the nested Bethe Ansatz is constructed for the case of A_2 rational spin chain. The structure and properties of these associated solutions are more various then in the case of usual XXX (A_1) spin…

High Energy Physics - Theory · Physics 2009-10-31 G. P. Pronko , Yu. G. Stroganov

We reformulate nested relations between off-shell $U_q(\widehat{\mathfrak{gl}}_N)$ Bethe vectors as a certain equation on generating series of strings of the composed $U_q(\widehat{\mathfrak{gl}}_N)$ currents. Using inversion of the…

Quantum Algebra · Mathematics 2008-11-24 Sergey Khoroshkin , Stanislav Pakuliak

We present an "algebraic treatment" of the analytical Bethe Ansatz. For this purpose, we introduce abstract monodromy and transfer matrices which provide an algebraic framework for the analytical Bethe Ansatz. It allows us to deal with a…

Mathematical Physics · Physics 2011-02-16 Daniel Arnaudon , Nicolas Crampe , Anastasia Doikou , Luc Frappat , Eric Ragoucy

We present an ``algebraic treatment'' of the analytical Bethe ansatz for open spin chains with soliton non preserving (SNP) boundary conditions. For this purpose, we introduce abstract monodromy and transfer matrices which provide an…

Mathematical Physics · Physics 2009-11-11 D. Arnaudon , N. Crampe , A. Doikou , L. Frappat , E. Ragoucy

We use the algebraic Bethe ansatz to obtain the eigenvalues and eigenvectors of the spin-1 Temperley-Lieb open quantum chain with "free" boundary conditions. We exploit the associated reflection algebra in order to prove the off-shell…

Mathematical Physics · Physics 2016-10-04 Rafael I. Nepomechie , Rodrigo A. Pimenta

We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using…

Mathematical Physics · Physics 2015-02-03 Nicolas Crampe

We diagonalize Q-operators for rational homogeneous sl(2)-invariant Heisenberg spin chains using the algebraic Bethe ansatz. After deriving the fundamental commutation relations relevant for this case from the Yang-Baxter equation we…

Mathematical Physics · Physics 2017-11-28 Rouven Frassek

We study the highest weight representations of the RTT--algebras for the R--matrix sp(4) type by the nested algebraic Bethe ansatz. These models were solved by Reshetikhin for sp(2n) but using a very special type of representation. The…

Mathematical Physics · Physics 2018-11-14 Cestmir Burdik , Ondrej Navratil

We give a detailed description of the nested algebraic Bethe ansatz. We consider integrable models with a $\mathfrak{gl}_3$-invariant $R$-matrix as the basic example, however, we also describe possible generalizations. We give recursions…

Mathematical Physics · Physics 2020-09-02 N. A. Slavnov

We study Olshanski twisted Yangian based models, known as one-dimensional "soliton non-preserving" open spin chains, by means of algebraic Bethe ansatz. The even case, when the bulk symmetry is $\mathfrak{gl}_{2n}$ and the boundary symmetry…

Mathematical Physics · Physics 2024-10-01 Vidas Regelskis

We propose a new approach to the spinor-spinor R-matrix with orthogonal and symplectic symmetry. Based on this approach and the fusion method we relate the spinor-vector and vector-vector monodromy matrices for quantum spin chains. We…

Mathematical Physics · Physics 2020-04-22 D. Karakhanyan , R. Kirschner

The off-diagonal Bethe ansatz method is generalized to the integrable model associated with the $sp(4)$ (or $C_2$) Lie algebra. By using the fusion technique, we obtain the complete operator product identities among the fused transfer…

Mathematical Physics · Physics 2019-06-05 Guang-Liang Li , Junpeng Cao , Panpan Xue , Zhi-Rong Xin , Kun Hao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The…

High Energy Physics - Theory · Physics 2023-07-18 Dmitry Chernyak , Azat M. Gainutdinov , Jesper Lykke Jacobsen , Hubert Saleur

The modified algebraic Bethe ansatz, introduced by Cramp\'e and the author [8], is used to characterize the spectral problem of the Heisenberg XXZ spin-$\frac{1}{2}$ chain on the segment with lower and upper triangular boundaries. The…

Mathematical Physics · Physics 2015-01-19 Samuel Belliard

We propose a generalization of the algebraic Bethe ansatz to obtain the eigenvectors of the Heisenberg spin chain with general boundaries associated to the eigenvalues and the Bethe equations found recently by Cao et al. The ansatz takes…

Mathematical Physics · Physics 2013-11-25 Samuel Belliard , Nicolas Crampé