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Related papers: Analytical Bethe ansatz in gl(N) spin chains

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We propose a new framework for the nested algebraic Bethe ansatz for a closed, rational spin chain with $\mathfrak{g}$-symmetry for any simple Lie algebra $\mathfrak{g}$. Starting the nesting process by removing a single simple root from…

Mathematical Physics · Physics 2024-06-12 Allan John Gerrard

The $so(5)$ (i.e., $B_2$) quantum integrable spin chains with both periodic and non-diagonal boundaries are studied via the off-diagonal Bethe Ansatz method. By using the fusion technique, sufficient operator product identities (comparing…

Mathematical Physics · Physics 2019-09-18 Guang-Liang Li , Junpeng Cao , Panpan Xue , Kun Hao , Pei Sun , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We consider the case of an integrable quantum spin chain with "soliton non-peserving" boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

High Energy Physics - Theory · Physics 2008-11-26 Anastasia Doikou

The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused…

Statistical Mechanics · Physics 2015-07-16 Junpeng Cao , Wen-Li Yang , Kangjie Shi , Yupeng Wang

We consider the integrable open XX quantum spin chain with nondiagonal boundary terms. We derive an exact inversion identity, using which we obtain the eigenvalues of the transfer matrix and the Bethe Ansatz equations. For generic values of…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

We generalise the fusion procedure for the $A_{\n-1}^{(1)}$ open spin chain ($\n>2$) and we show that the transfer matrix satisfies a crossing property. We use these results to solve the $A_{\n-1}^{(1)}$ open spin chain with $U_{q}…

High Energy Physics - Theory · Physics 2008-11-26 Anastasia Doikou

We study open spin chains based on rational sl(N) and sl(M|N) R-matrices. We classify the solutions of the reflection equations, for both the soliton-preserving and soliton-non-preserving cases. We then write the Bethe equations for these…

Mathematical Physics · Physics 2007-05-23 D. Arnaudon , J. Avan , N. Crampe' , A. Doikou , L. Frappat , E. Ragoucy

We consider the case of an integrable quantum spin chain with ``soliton non-preserving'' boundary conditions. This is the first time that such boundary conditions have been considered in the spin chain framework. We construct the transfer…

High Energy Physics - Theory · Physics 2007-05-23 Anastasia Doikou

We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one…

Mathematical Physics · Physics 2020-08-25 Etienne Granet , Jesper Lykke Jacobsen , Hubert Saleur

We propose a set of conventional Bethe Ansatz equations and a corresponding expression for the eigenvalues of the transfer matrix for the open spin-1/2 XXZ quantum spin chain with nondiagonal boundary terms, provided that the boundary…

High Energy Physics - Theory · Physics 2008-11-26 Rafael I. Nepomechie

The nested off-diagonal Bethe ansatz is generalized to study the quantum spin chain associated with the $SU_q(3)$ R-matrix and generic integrable non-diagonal boundary conditions. By using the fusion technique, certain closed operator…

Mathematical Physics · Physics 2016-08-24 Guang-Liang Li , Junpeng Cao , Kun Hao , Fakai Wen , Wen-Li Yang , Kangjie Shi

We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…

Mathematical Physics · Physics 2014-10-23 N. Cirilo António , N. Manojlović , I. Salom

We give a pedagogical introduction to the Bethe ansatz techniques in integrable QFTs and spin chains. We first discuss and motivate the general framework of asymptotic Bethe ansatz for the spectrum of integrable QFTs in large volume, based…

High Energy Physics - Theory · Physics 2016-07-26 Fedor Levkovich-Maslyuk

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

We solve the spectrum of quantum spin chains based on representations of the Temperley-Lieb algebra associated with the quantum groups ${\cal U}% _{q}(X_{n})$ for $X_{n}=A_{1},$ $B_{n},$ $C_{n}$ and $D_{n}$. The tool is a modified version…

Exactly Solvable and Integrable Systems · Physics 2016-12-28 R. C. T. Ghiotto , A. L. Malvezzi

The spin-1/2 XYZ model with both periodic and anti-periodic boundary conditions is studied via the off-diagonal Bethe ansatz method. The exact spectra of the Hamiltonians and the Bethe ansatz equations are derived by constructing the…

Statistical Mechanics · Physics 2015-06-16 Junpeng Cao , Shuai Cui , Wen-Li Yang , Kangjie Shi , Yupeng Wang

In this paper we study the spectrum of the spin-1 Temperley-Lieb spin chain with integrable open boundary conditions. We obtain the eigenvalue expressions as well as its associated Bethe ansatz equations by means of the coordinate Bethe…

Exactly Solvable and Integrable Systems · Physics 2013-06-25 G. A. P. Ribeiro , A. Lima-Santos

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 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 present a procedure to extract the generalised eigenvectors of a non-diagonalisable matrix by considering a diagonalisable perturbation of it and computing the non-diagonalisable limit of its eigenvectors. As an example of this process,…

High Energy Physics - Theory · Physics 2022-07-13 Juan Miguel Nieto García , Leander Wyss