Related papers: The algebraic Bethe ansatz for open A_{2n}^{(2)} v…
In this paper, the algebraic Bethe ansatz with periodic boundary conditions is used to investigate trigonometric vertex models associated with the fundamental representations of the non-exceptional Lie algebras. This formulation allow us to…
By combining the algebraic Bethe ansatz and the off-diagonal Bethe ansatz, we investigate the trigonometric SU(3) model with generic open boundaries. The eigenvalues of the transfer matrix are given in terms of an inhomogeneous T-Q…
We present a supermatrix realisation of q-deformed spinor-spinor and spinor-vector R-matrices. These R-matrices are then used to construct transfer matrices for $U_{q^2}(\mathfrak{so}_{2n+1})$- and $U_{q}(\mathfrak{so}_{2n+2})$-symmetric…
In this paper we study isotropic integrable systems based on the braid-monoid algebra. These systems constitute a large family of rational multistate vertex models and are realized in terms of the B_n, C_n and D_n Lie algebra and by the…
We consider the Bethe ansatz solution of integrable models interacting through factorized $S$-matrices based on the central extention of the $\bf{su}(2|2)$ symmetry. The respective $\bf{su}(2|2)$ $R$-matrix is explicitly related to that of…
The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of…
We study the exact solution of quantum integrable system associated with the $A^{(2)}_3$ twist Lie algebra, where the boundary reflection matrices have non-diagonal elements thus the $U(1)$ symmetry is broken. With the help of the fusion…
The Gaudin model based on the sl_2-invariant r-matrix with an extra Jordanian term depending on the spectral parameters is considered. The appropriate creation operators defining the Bethe states of the system are constructed through a…
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 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…
The one-dimensional small-polaron model with open boundary conditions is considered in the framework of the quantum inverse scattering method. The spin model which is equivalent to the small-polaron model is the Heisenberg $XXZ$ spin chain…
For generic values of q, all the eigenvectors of the transfer matrix of the U_q sl(2)-invariant open spin-1/2 XXZ chain with finite length N can be constructed using the algebraic Bethe ansatz (ABA) formalism of Sklyanin. However, when q is…
We study quantum integrable models with GL(3) trigonometric $R$-matrix and solvable by the nested algebraic Bethe ansatz. Using the presentation of the universal Bethe vectors in terms of projections of products of the currents of the…
Analytic Bethe ansatz is executed for a wide class of finite dimensional $U_q(B^{(1)}_r)$ modules. They are labeled by skew-Young diagrams which, in general, contain a fragment corresponding to the spin representation. For the transfer…
We have constructed and solved various one-dimensional quantum mechanical models which have quantum algebra symmetry. Here we summarize this work, and also present new results on graded models, and on the so-called string solutions of the…
Several quantum many-body models in one dimension possess exact solutions via the Bethe ansatz method, which has been highly successful for understanding their behavior. Nevertheless, there remain physical properties of such models for…
The Bethe ansatz equations of the 1-D SU(3) Hubbard model are systematically derived by diagonalizing the inhomogeneous transfer matrix of the XXX model. We first derive the scattering matrix of the SU(3) Hubbard model through the…
We investigate various aspects of the integrability of the vertex models associated to the $D_n^2$ affine Lie algebra with open boundaries. We first study the solutions of the corresponding reflection equation compatible with the minimal…
The recently introduced two-parameter eight-state $U_q[gl(3|1)]$ supersymmetric fermion model is extended to include boundary terms. Nine classes of boundary conditions are constructed, all of which are shown to be integrable via the graded…
A system of U(N)-matrix difference equations is solved by means of a nested version of a generalized Bethe Ansatz. The highest weight property of the solutions is proved and some examples of solutions are calculated explicitly. (Part II of…