Related papers: Nested Bethe ansatz for "all" closed spin chains

We examine super symmetric representations of the B-type Hecke algebra. We exploit such representations to obtain new non-diagonal solutions of the reflection equation associated to the super algebra U_q(gl(m|n)). The boundary super algebra…

We study the integrable crosscap states of the integrable quantum spin chains and we classify them for the $\mathfrak{gl}(N)$ symmetric models. We also give a derivation for the exact overlaps between the integrable crosscap states and the…

This paper continues our recent studies on the algebraic Bethe ansatz for the RTT-algebras of sp($2n$) and o($2n$) types. In these studies, we encountered the RTT-algebras which we called An. The next step in our construction of the Bethe…

We introduce a generalization of the original Coordinate Bethe Ansatz that allows to treat the case of open spin chains with non-diagonal boundary matrices. We illustrate it on two cases: the XXX and XXZ chains. Short review on a joint work…

We discuss the possible extensions of Bethe/gauge correspondence to quantum integrable systems based on the super-Lie algebras of A type. Along the way we propose the analogues of Nakajima quiver varieties whose cohomology and K-theory…

We study the highest weight representations of the RTT--algebras for the R--matrix sp(4) type by the nested algebraic Bethe ansatz. These models were solved by Reshetikhin for sp(2n) but using a very special type of representation. The…

Based on the inhomogeneous T-Q relation and the associated Bethe Ansatz equations obtained via the off-diagonal Bethe Ansatz, we construct the Bethe-type eigenstates of the SU(2)-invariant spin-s chain with generic non-diagonal boundaries…

We study Olshanski twisted Yangian based models, known as one-dimensional "soliton non-preserving" open spin chains, by means of algebraic Bethe ansatz. The even case, when the bulk symmetry is $\mathfrak{gl}_{2n}$ and the boundary symmetry…

The Hoft structure of the central extension of the $U_q \left( \widehat{sl\left( n \right) }\right)$ algebra is considered. The intertwine matrix induces new integrable spin chain models. We show the relation of these models and the…

For non-simple laced Lie algebras, the $\text{B}_{N}$ and $\text{C}_{N}$ are Langlands dual to each other in mathematical. In this article, we give another Bethe/Gauge correspondence between 3d (or 2d) classical Lie group supersymmetry…

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…

We generalize our recent explicit construction of the full hierarchy of Baxter Q-operators of compact spin chains with su(n) symmetry to the supersymmetric case su(n|m). The method is based on novel degenerate solutions of the graded…

The off-diagonal Bethe ansatz method is generalized to the high spin integrable systems associated with the su(2) algebra by employing the spin-s isotropic Heisenberg chain model with generic integrable boundaries as an example. With the…

We derive by the traditional algebraic Bethe ansatz method the Bethe equations for the general open XXZ spin chain with non-diagonal boundary terms under the Nepomechie constraint [J. Phys. A 37 (2004), 433-440, arXiv:hep-th/0304092]. The…

A new, so called odd Gel'fand-Zetlin basis is introduced for the irreducible covariant tensor representations of the Lie superalgebra gl(n|n). The related Gel'fand-Zetlin patterns are based upon the decomposition according to a particular…

We develop a new method to compute the exact overlaps between integrable boundary states and on-shell Bethe states for integrable spin chains. Our method is based on the coordinate Bethe Ansatz and does not rely on the "rotation trick" of…

We diagonalize the transfer matrix of a solvable vertex model constructed by combining the vector representation of U_q[Sl(n|m)] and its dual by means of the quantum inverse scattering framework. The algebraic Bethe ansatz solution consider…

A quantum integrable spin chain model associated with the $G_2$ exceptional Lie algebra is studied. By using the fusion technique, the closed recursive relations among the fused transfer matrices are obtained. These identities allow us to…

Two branches of integrable open quantum-group invariant $D_{n+1}^{(2)}$ quantum spin chains are known. For one branch (epsilon=0), a complete Bethe ansatz solution has been proposed. However, the other branch (epsilon=1) has so far resisted…

We study Bethe vectors of integrable models based on the super-Yangian $Y(\mathfrak{gl}(m|n))$. Starting from the super-trace formula, we exhibit recursion relations for these vectors in the case of $Y(\mathfrak{gl}(2|1))$ and…