Related papers: On the ${\cal{U}}_{q}[sl(2)]$ Temperley-Lieb refle…
This work concerns to the studies of boundary integrability of the vertex models from representations of the Temperley-Lieb algebra associated with the quantum group ${\cal U}_{q}[X_{n}]$ for the affine Lie algebras $X_{n}$ = $A_{1}^{(1)}$,…
This work concerns the boundary integrability of the ${\cal{U}}_{q}[osp(1|2)]$ Temperley-Lieb model. We constructed the solutions of the graded reflection equations in order to determine the boundary terms of the correspondig spin-1…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the fundamental $U_q[G_2]$ vertex model. We find four distinct classes of reflection matrices such that half of them are diagonal while the other half…
We derive and classify all regular solutions of the boundary Yang-Baxter equation for 19-vertex models known as Zamolodchikov-Fateev or $A_{1}^{(1)}$ model, Izergin-Korepin or $A_{2}^{(2)}$ model, sl(2|1) model and osp(2|1) model. We find…
Integrable boundary conditions are studied for critical A-D-E and general graph-based lattice models of statistical mechanics. In particular, using techniques associated with the Temperley-Lieb algebra and fusion, a set of boundary…
In this paper I construct lattice models with an underlying $U_q osp(2,2)$ superalgebra symmetry. I find new solutions to the graded Yang-Baxter equation. These {\it trigonometric} $R$-matrices depend on {\it three} continuous parameters,…
In this paper we consider families of multiparametric $R$-matrices to make a systematic study of the boundary Yang-Baxter equations in order to discuss the corresponding families of multiparametric $K$-matrices. Our results are indeed…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $A_{n-1}^{(1)}$ affine Lie algebra. We have classified them in two classes of solutions. The first class consists…
In this paper, we address the problem of Yang-Baxter integrability of doubled quantum circuit of qubits (spins 1/2) with open boundary conditions where the two circuit replicas are only coupled at the left or right boundary. We investigate…
We derive and classify all solutions of the boundary Yang-Baxter equation (or the reflection equation) for the 19-vertex model associated with $U_q(\widehat{sl_2})$. Integrable $XXZ$ spin-1 chain hamiltonian with general boundary…
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the graded version of the $A_{n-1}^{(1)}$ affine Lie algebra, the $U_{q}[sl(m|n)^{(1)}]$ vertex model, also known as…
The spectral decomposition of regular Uq(sl_2)-invariant solutions of the Yang-Baxter equation is studied. An algorithm for finding all possible solutions of spin s is developed. It also allows to reconstruct the R-matrix from a given…
The general solutions of the reflection equation associated with Temperley-Lieb $R$-matrices are constructed. Their parametrization is defined and the Hamiltonians of corresponding integrable spin systems are given.
We investigate the possible regular solutions of the boundary Yang-Baxter equation for the vertex models associated to the D_{n+1}^(2) affine Lie algebra. We have classified them in terms of three types of K-matrices. The first one have n+2…
We investigate the regular solutions of the boundary Yang-Baxter equation for the vertex models associated with the $B_{n}^{(1)}$ and $A_{2n}^{(2)}$ affine Lie algebras. In both class of models we find two general solutions with $n+1$ free…
We derive the solutions of the boundary Yang-Baxter equation associated with a supersymmetric nineteen vertex model constructed from the three-dimensional representation of the twisted quantum affine Lie superalgebra…
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…
A strongly correlated electron system associated with the quantum superalgebra ${U}_q[{osp}(2|2)]$ is studied in the framework of the quantum inverse scattering method. By solving the graded reflection equation, two classes of…
In this paper, several proposals of optically simulating Yang-Baxter equations have been presented. Motivated by the recent development of anyon theory, we apply Temperley-Lieb algebra as a bridge to recast four-dimentional Yang-Baxter…
We study the boundary integrability problem of the massless sector of $AdS_3 \times S^3 \times T^4 $ string theory. Exploiting the difference-form of the massless scattering theory, we find a very simple and exhaustive list of reflection…