Related papers: On the Exact Solution of Models based on Non-Stand…
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…
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…
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…
Integrable open quantum spin-chain transfer matrices constructed from trigonometric R-matrices associated to affine Lie algebras $\hat g$, and from certain K-matrices (reflection matrices) depending on a discrete parameter p, were recently…
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…
We investigate two solvable models for Bose-Einstein condensates and extract physical information by studying the structure of the solutions of their Bethe ansatz equations. A careful observation of these solutions for the ground state of…
Quantum doubles of finite group algebras form a class of quasi-triangular Hopf algebras which algebraically solve the Yang--Baxter equation. Each representation of the quantum double then gives a matrix solution of the Yang--Baxter…
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called…
The thermodynamic Bethe Ansatz equations that have been proposed to describe massive integrable deformations of the coset conformal field theories $g_k\times g_l/g_{k+l}$ are shown to result directly by applying the usual thermodynamic…
Stationary probability distributions for stochastic processes on linear chains with closed or open ends are obtained using the matrix product Ansatz. The matrices are representations of some quadratic algebras. The algebras and the types of…
We formulate in terms of the quantum inverse scattering method the exact solution of a $spl(2|1)$ invariant vertex model recently introduced in the literature. The corresponding transfer matrix is diagonalized by using the algebraic…
An analytic Bethe ansatz is carried out related to the Lie superalgebra osp(1|2s). We present an eigenvalue formula of a transfer matrix in dressed vacuum form (DVF) labeled by a Young (super) diagram. Remarkable duality among DVFs is…
We construct integrable generalised models in a systematic way exploring different representations of the gl(N) algebra. The models are then interpreted in the context of atomic and molecular physics, most of them related to different types…
The implementation of the algebraic Bethe ansatz for the XXZ Heisenberg spin chain, of arbitrary spin-$s$, in the case, when both reflection matrices have the upper-triangular form is analyzed. The general form of the Bethe vectors is…
An integral presentation for the scalar products of nested Bethe vectors for the quantum integrable models associated with the quantum affine algebra $U_q(\hat{\mathfrak{gl}}_3)$ is given. This result is obtained in the framework of the…
The eigenvalues of the elliptic N-body Ruijsenaars operator are obtained by a dynamical version of the algebraic nested Bethe ansatz method. We use a result of Felder and Varchenko, who showed how to obtain the Ruijsenaars operator as the…
In these lectures the introduction to algebraic aspects of Bethe Ansatz is given. The applications to the seminal spin 1/2 XXX model is discussed in detail and the generalization to higher spin as well as XXZ and lattice Sine-Gordon model…
We classify trigonometric solutions to the associative Yang-Baxter equation (AYBE) for A = Mat_n, the associative algebra of n-by-n matrices. The AYBE was first presented in a 2000 article by Marcelo Aguiar and also independently by…
We describe the Algebraic Bethe Ansatz for the spin-1/2 XXX and XXZ Heisenberg chains with open and periodic boundary conditions in terms of tensor networks. These Bethe eigenstates have the structure of Matrix Product States with a…
For the Bernoulli Matching model of sequence alignment problem we apply the Bethe ansatz technique via an exact mapping to the 5--vertex model on a square lattice. Considering the terrace--like representation of the sequence alignment…