Related papers: Bethe Ansatz Equations for the Broken $Z_{N}$-Symm…
We study the one-dimensional totally asymmetric simple exclusion process in contact with two reservoirs including also a fugacity at one boundary. The eigenvectors and the eigenvalues of the corresponding Markov matrix are computed using…
Two distinct $\eta$-deformations of strings on AdS$_5\times$S$^5$ can be defined; both amount to integrable quantum deformations of the string non-linear sigma model, but only one is itself a superstring background. In this paper we compare…
Based on the rational R-matrix of the supersymmetric sl(2,1) matrix difference equations are solved by means of a generalization of the nested algebraic Bethe ansatz. These solutions are shown to be of highest-weight with respect to the…
We analyze the Bethe ansatz equations describing the complete spectrum of the transition matrix of the partially asymmetric exclusion process on a finite lattice and with the most general open boundary conditions. We extend results obtained…
In this text, we provide a detailed exposition of the Algebraic Bethe ansatz for square ice (or six vertex model), which allows the construction of candidate eigenvectors for the transfer matrices of this model. We also prove some formula…
We examine the commuting elements $\theta_i=\sum_{j\neq i} \frac{s_{ij}}{z_i-z_j}$, $z_i\neq z_j$, $s_{ij}$ the transposition swapping $i$ and $j$, and we study their actions on irreducible $S_n$ representations. By applying Schur-Weyl…
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 present the Bethe ansatz solution for the discrete time zero range and asymmetric exclusion processes with fully parallel dynamics. The model depends on two parameters: $p$, the probability of single particle hopping, and $q$, the…
We consider the problem of analytically continuing energies computed with the Bethe ansatz, as posed by the study of non-compact integrable spin chains. By introducing an imaginary extensive twist in the Bethe equations, we show that one…
We present the analytical Bethe ansatz for spin chains based on the superalgebras gl(M|N), $M\neq N$, with at each site an arbitrary representation (and including inhomogeneities). The calculation is done for closed and open spin chains. In…
We consider the exact solution of a model of correlated particles, which is presented as a system of interacting XX and Fateev-Zamolodchikov chains. This model can also be considered as a generalization of the multiband anisotropic $t-J$…
An integrable version of the supersymmetric U model with open boundary conditions and an impurity situated at one end of the chain is introduced. The model is solved through the algebraic Bethe ansatz method and the Bethe ansatz equations…
The algebraic structure underlying the totally asymmetric exclusion process is studied by using the Bethe Ansatz technique. From the properties of the algebra generated by the local jump operators, we explicitly construct the hierarchy of…
The semi-classical limit of the algebraic Bethe Ansatz method is used to solve the theory of Gaudin models. Via the off-shell method we find the spectra and eigenvectors of the N-1 independent Gaudin Hamiltonians with symmetry osp(2|1). We…
The exact solution for the energy spectrum of a one-dimensional Hamiltonian with local two-site interactions and periodic boundary conditions is determined. The two-site Hamiltonians commute with the symmetry algebra given by the Drinfeld…
The Bethe ansatz represents an analytical method enabling the exact solution of numerous models in condensed matter physics and statistical mechanics. When a global symmetry is present, the trial wavefunctions of the Bethe ansatz consist of…
In this article we have discovered a close relationship between the (algebraic) Bethe Ansatz equations of the spin $s$ XXZ model of a finite size and the $q$-Sturm-Liouville problem. We have demonstrated that solutions of the Bethe Ansatz…
We implement fully the algebraic Bethe ansatz for the XXX Heisenberg spin chain in the case when both boundary matrices can be brought to the upper-triangular form. We define the Bethe vectors which yield the strikingly simple expression…
A scattering scattering description is proposed for a boundary perturbation of a c=1 SL(2,Z) invariant conformal field theory. The bulk massless S-matrices are of the form of Zamolodchikov's staircase model. Using the boundary version of…
A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It…