Related papers: General scalar products in the arbitrary six-verte…
Within the Matrix Product Formalism we have already introduced a multi- species exclusion process in which different particles hop with different rates and fast particles stochastically overtake slow ones. In this letter we show that on an…
We connect two alternative concepts of solving integrable models, Baxter's method of auxiliary matrices (or Q-operators) and the algebraic Bethe ansatz. The main steps of the calculation are performed in a general setting and a formula for…
We describe a logarithmic tensor product theory for certain module categories for a ``conformal vertex algebra.'' In this theory, which is a natural, although intricate, generalization of earlier work of Huang and Lepowsky, we do not…
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 SU(3)-invariant integrable models solvable by nested algebraic Bethe ansatz. We obtain a determinant representation for particular case of scalar products of Bethe vectors. This representation can be used for the calculation of…
We generalize the tensor product theory for modules for a vertex operator algebra previously developed in a series of papers by the first two authors to suitable module categories for a ``conformal vertex algebra'' or even more generally,…
This is an expository paper on tensor products where the standard approaches for constructing concrete instances of algebraic tensor products of linear spaces, via quotient spaces or via linear maps of bilinear maps, are reviewed by…
We derive the recursive relations of the partition function for the eight-vertex model on an $N\times N$ square lattice with domain wall boundary condition. Solving the recursive relations, we obtain the explicit expression of the domain…
We derive a number of results related to the Gaudin model associated to the simple Lie algebra of type G$_2$. We compute explicit formulas for solutions of the Bethe ansatz equations associated to the tensor product of an arbitrary…
We can recast the Yang-Baxter equation as a triple product equation. Assuming the triple product to satisfy some algebraic relations, we can find new solutions of the Yang-Baxter equation. This program has been completed here for the…
For a particular set of Boltzmann weights and a particular boundary condition for the six vertex model in statistical mechanics, we compute explicitly the partition function and show it to be equal to a factorial Schur function, giving a…
We derive the coordinate space wave function for the inhomogeneous six-vertex model from the Algebraic Bethe Ansatz. The result is in agreement with the result first obtained long time ago by Yang and Gaudin in the context of the problem of…
We consider the trigonometric Felderhof model, of free fermions in an external field, on a finite lattice with domain wall boundary conditions. The vertex weights are functions of rapidities and external fields. We obtain a determinant…
The algebraic Bethe ansatz is a powerful method to diagonalize transfer-matrices of statistical models derived from solutions of (graded) Yang Baxter equations, connected to fundamental representations of Lie (super-)algebras and their…
In the theory of dynamical Yang-Baxter equation, with any Hopf algebra $H$ and a certain $H$-module and $H$-comodule algebra $L$ (base algebra) one associates a monoidal category. Given an algebra $A$ in that category, one can construct an…
We develop a unified formulation of the quantum inverse scattering method for lattice vertex models associated to the non-exceptional $A^{(2)}_{2r}$, $A^{(2)}_{2r-1}$, $B^{(1)}_r$, $C^{(1)}_r$, $D^{(1)}_{r+1}$ and $D^{(2)}_{r+1}$ Lie…
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.…
We consider the problem of the exact computation of the correlation functions of the eight-vertex solid-on-solid model by means of the algebraic Bethe Ansatz. We compute the scalar product between a Bethe eigenstate and an arbitrary state…
The algebraic Bethe Ansatz is a prosperous and well-established method for solving one-dimensional quantum models exactly. The solution of the complex eigenvalue problem is thereby reduced to the solution of a set of algebraic equations.…
Solutions of the classical Yang-Baxter equation provide a systematic method to construct integrable quantum systems in an algebraic manner. A Lie algebra can be associated with any solution of the classical Yang--Baxter equation, from which…