Related papers: Noncompact sl(N) spin chains: BGG-resolution, Q-op…
We formulate the algebraic Bethe ansatz solution of the SU(N) vertex models with rather general non-diagonal toroidal boundary conditions. The reference states needed in the Bethe ansatz construction are found by performing gauge…
We present a family of novel Lax operators corresponding to representations of the RTT-realisation of the Yangian associated with $D$-type Lie algebras. These Lax operators are of oscillator type, i.e. one space of the operators is…
We construct boundary type operators satisfying fused reflection equation for arbitrary representations of the Baxterized affine Hecke algebra. These operators are analogues of the fused reflection matrices in solvable half-line spin chain…
The spectral properties of operators formed from generators of the q-Onsager non-Abelian infinite dimensional algebra are investigated. Using a suitable functional representation, all eigenfunctions are shown to obey a second-order…
We consider the open spin-s XXZ quantum spin chain with nondiagonal boundary terms. By exploiting certain functional relations at roots of unity, we derive a generalized form of T-Q relation involving more than one independent Q(u), which…
Let $A_q$ be the alternating central extension of the q-Onsager algebra, a comodule algebra over the quantum loop algebra of $sl_2$. We classify one-dimensional representations of $A_q$, and show that spin-j K-operators constructed in…
We find explicit expressions for two first finite size corrections to the distribution of Bethe roots, the asymptotics of energy and high conserved charges in the sl(2) quantum Heisenberg spin chain of length J in the thermodynamical limit…
We study representation theory of Drinfel'd twists, in terms of what we call F matrices, associated to finite dimensional irreducible modules of quantum affine algebras, and which factorize the corresponding (unitary) R matrices. We…
We consider the sl(2)_q-invariant open spin-1/2 XXZ quantum spin chain of finite length N. For the case that q is a root of unity, we propose a formula for the number of admissible solutions of the Bethe ansatz equations in terms of…
We propose Wronskian-like determinant formulae for the Baxter Q-functions and the eigenvalues of transfer matrices for spin chains related to the quantum affine superalgebra U_{q}(hat{gl}(M|N)). In contrast to the supersymmetric…
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…
Based on the conjecture for the exact eigenvalue of the transfer matrix of the higher half-integer spin XXZ chain at the Razumov-Stroganov point, we evaluate the corresponding Baxter's Q operator in closed form by solving the TQ equation.…
The spin-1/2 Heisenberg XXZ chain is a paradigmatic quantum integrable model. Although it can be solved exactly via Bethe ansatz techniques, there are still open issues regarding the spectrum at root of unity values of the anisotropy. We…
We consider quantum quenches in the integrable $SU(3)$-invariant spin chain (Lai-Sutherland model), and focus on the family of integrable initial states. By means of a Quantum Transfer Matrix approach, these can be related to…
We propose that Baxter's Z-invariant six-vertex model at the rational gl(2) point on a planar but in general not rectangular lattice provides a way to study Yangian invariants. These are identified with eigenfunctions of certain monodromies…
We consider linear bounded operators acting in Banach spaces with a basis, such operators can be represented by an infinite matrix. We prove that for an invertible operator there exists a sequence of invertible finite-dimensional operators…
We consider a class of asymptotic representations of the Borel subalgebra of the quantum affine superalgebra U_q(gl(M|N)^). This is characterized by Drinfeld rational fractions. In particular, we consider contractions of U_q(gl(M|N)) in 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…
Starting from the Verma module of U_q sl(2) we consider the evaluation module for affine U_q sl(2) and discuss its crystal limit (q=0). There exists an associated integrable statistical mechanics model on a square lattice defined in terms…
We demonstrate that the Q matrix introduced in Baxter's 1972 solution of the eight vertex model has some eigenvectors which are not eigenvectors of the spin reflection operator and conjecture a new functional equation for Q(v) which both…