Related papers: SU(N) Matrix Difference Equations and a Nested Bet…
The double row transfer matrix of the open O(N) spin chain is diagonalized and the Bethe Ansatz equations are also derived by the algebraic Bethe Ansatz method including the so far missing case when the residual symmetry is…
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}…
We have recently constructed a large class of open quantum spin chains which have quantum-algebra symmetry and which are integrable. We show here that these models can be exactly solved using a generalization of the analytical Bethe Ansatz…
We present in an unified and detailed way the nested Bethe ansatz for open spin chains based on Y(gl(\fn)), Y(gl(\fm|\fn)), U_{q}(gl(\fn)) or U_{q}(gl(\fm|\fn)) (super)algebras, with arbitrary representations (i.e. `spins') on each site of…
The three different sets of Bethe ansatz equations describing the Bethe ansatz solution of the supersymmetric t-J model are known to be equivalent. Here we give a new, simplified proof of this fact which relies on the properties of certain…
We consider universal off-shell Bethe vectors given in terms of Drinfeld realization of the algebra $U_q(\widehat{gl}_N)$ [arXiv:math/0610517,arXiv:0711.2819]. We investigate ordering properties of the product of the transfer matrix and…
We consider a generalized model with SU(3)-invariant R-matrix, and review the nested Bethe Ansatz for constructing eigenvectors of the transfer matrix. A sum formula for the scalar product between generic Bethe vectors, originally obtained…
New classes of integrable boundary conditions for the q-deformed (or two-parameter) supersymmetric U model are presented. The boundary systems are solved by using the coordinate space Bethe ansatz technique and Bethe ansatz equations are…
We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…
A class of integrable boundary terms for the eight-state supersymmtric $U$ model are presented by solving the graded reflection equations. The boundary model is solved by using the coordinate Bethe ansatz method and the Bethe ansatz…
In this proceeding we present the nested Bethe ansatz for open spin chains of XXX-type, with arbitrary representations (i.e. `spins') on each site of the chain and diagonal boundary matrices $(K^+(u),K^-(u))$. The nested Bethe anstaz…
Finite difference schemes are here solved by means of a linear matrix equation. The theoretical study of the related algebraic system is exposed, and enables us to minimize the error due to a finite difference approximation.
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…
An ASEP with two species of particles and different hopping rates is considered on a ring. Its integrability is proved and the Nested Algebraic Bethe Ansatz is used to derive the Bethe Equations for states with arbitrary numbers of…
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…
We reformulate the nested coordinate Bethe ansatz in terms of coproducts of Yangian symmetry generators. This allows us to derive the nested Bethe equations for the bound state string S-matrices. We find that they coincide with the Bethe…
The quantum integrability is established for the one-dimensional supersymmetric $U$ model with boundary terms by means of the quantum inverse scattering method. The boundary supersymmetric $U$ chain is solved by using the coordinate space…
We study quantum Uq(gl(N)) integrable models solvable by the nested algebraic Bethe ansatz. Different formulas are given for the right and left universal off-shell nested Bethe vectors. It is shown that these formulas can be related by…
The missing label for basis vectors of $SU(3)$ representations corresponding to the reduction $SU(3) \supset SO(3)$ can be provided by the eigenvalues of $SO(3)$ scalars in the enveloping algebra of $su(3)$. There are only two such…
We derive the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process with the most general open boundary conditions. For totally asymmetric diffusion we calculate the…