Related papers: GL(3)-Based Quantum Integrable Composite Models. I…
The general expression for the local matrix $L(\theta)$ of a quantum chain with the site space in any representation of $su(3)$ is obtained. This is made by generalizing $L(\theta)$ from the fundamental representation and imposing the…
We study quantum integrable models with GL(3) trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. Scalar products of Bethe vectors in such models can be expressed in terms of a bilinear combination of the highest…
We apply the algebraic Bethe ansatz developed in our previous paper \cite{CM} to three different families of U(1) integrable vertex models with arbitrary $N$ bond states. These statistical mechanics systems are based on the higher spin…
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…
An integrable Kondo problem in the one-dimensional supersymmetric t-J model is studied by means of the boundary supersymmetric quantum inverse scattering method. The boundary $K$ matrices depending on the local moments of the impurities are…
Three kinds of integrable Kondo problems in one-dimensional extended Hubbard models are studied by means of the boundary graded quantum inverse scattering method. The boundary K matrices depending on the local moments of the impurities are…
We consider an open spin chain model with GL(N) bulk symmetry that is broken to GL(M) x GL(N-M) by the boundary, which is a generalization of a model arising in string/gauge theory. We prove the integrability of this model by constructing…
We propose new inhomogeneous local integrability equations - combined equations, for statistical vertex models of general dimensions in the framework of the Algebraic Bethe Ansatz (ABA). For the low dimensional cases the efficiency of the…
The general expression for the local matrix $t(\theta)$ of a quantum chain with the site space in any representation of su(3) is obtained. This is made by generalizing $t(\theta)$ from the fundamental representation and imposing the…
Supersymmetric composite generalized quantum integrable models solvable by the algebraic Bethe ansatz are studied. Using a coproduct in the bialgebra of monodromy matrix elements and their action on Bethe vectors, formulas for Bethe vectors…
This work is concerned with the formulation of the graded quantum inverse scattering method for a class oflattice models with reflecting boundary conditions. The $sl(2|1)^{(2)}$ and $osp(2|1)$ models are considered with their diagonal…
We consider integrable models solved by the nested algebraic Bethe ansatz and associated with $\mathfrak{gl}(2|1)$ or $\mathfrak{gl}(3)$ algebra symmetry. The analogue of sum formulae, previously formulated for scalar products, is…
The labelling of states of irreducible representations of GL(3) in an O(3) basis is well known to require the addition of a single O(3)-invariant operator, to the standard diagonalisable set of Casimir operators in the subgroup chain GL(3)…
A general model independent approach using the `off-shell Bethe Ansatz' is presented to obtain an integral representation of generalized form factors. The general techniques are applied to the quantum sine-Gordon model alias the massive…
We generalize the nested off-diagonal Bethe ansatz method to study the quantum chain associated with the twisted $D^{(2)}_3$ algebra (or the $D^{(2)}_3$ model) with either periodic or integrable open boundary conditions. We obtain the…
Four dimensional irreducible representations of the superalgebra gl(2,1) carry a free parameter. We compute the spectra of the corresponding transfer matrices by means of the nested algebraic Bethe ansatz together with a generalized fusion…
Integrable extended Hubbard models arising from symmetric group solutions are examined in the framework of the graded Quantum Inverse Scattering Method. The Bethe ansatz equations for all these models are derived by using the algebraic…
The algebraic Bethe ansatz can be performed rather abstractly for whole classes of models sharing the same $R$-matrix, the only prerequisite being the existence of an appropriate pseudo vacuum state. Here we perform the algebraic Bethe…
We consider quantum integrable models with $\mathfrak{gl}(2|1)$ symmetry. We derive a set of multiple commutation relations between the monodromy matrix entries. These multiple commutation relations allow us to obtain different…
We solve the gl(1|2) generalized model by means of the algebraic Bethe ansatz. The resulting eigenvalue of the transfer matrix and the Bethe ansatz equations depend on three complex functions, called the parameters of the generalized model.…