Related papers: Separation of variables for integrable spin-boson …
The generalization of the Yang-Baxter equations (YBE) in the presence of Z_2 grading along both chain and time directions is presented. The XXZ model with staggered disposition along a chain of both, the anisotropy \pm\Delta, as well as…
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…
The formulation and resolution of integrable lattice statistical models in a quantum group covariant way is the subject of this review. The Bethe Ansatz turns to be remarkably useful to implement quantum group symmetries and to provide…
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 diagonalise the Hamiltonian of the Temperley-Lieb loop model with open boundaries using a coordinate Bethe Ansatz calculation. We find that in the groundstate sector of the loop Hamiltonian, but not in other sectors, a certain constraint…
We study the P"oschl-Teller equation in complex domain and deduce infinite families of TQ and Bethe ansatz equations, classified by four integers. In all these models the form of T is very simple, while Q can be explicitly written in terms…
We study the spectrum of the scaling Lee-Yang model on a finite interval from two points of view: via a generalisation of the truncated conformal space approach to systems with boundaries, and via the boundary thermodynamic Bethe ansatz.…
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…
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 develop a new approach to Baxter Q-operators by relating them to the theory of Yangians, which are the simplest examples for quantum groups. Here we open up a new chapter in this theory and study certain degenerate solutions of the…
Recently, researchers have proposed the Asymmetric Bethe ansatz method - a theoretical tool that extends the scope of Bethe ansatz-solvable models by "breaking" partial mirror symmetry via the introduction of a fully reflecting boundary.…
We study an integrable vertex model with a periodic boundary condition associated with U_q(A_n^{(1)}) at the crystallizing point q=0. It is an (n+1)-state cellular automaton describing the factorized scattering of solitons. The dynamics…
The Functional Bethe Ansatz (FBA) proposed by Sklyanin is a method which gives separation variables for systems for which an $R$-matrix is known. Previously the FBA was only known for $SL(2)$ and $SL(3)$ (and associated) $R$-matrices. In…
In this contribution we review the theory of integrability of quantum systems in one spatial dimension. We introduce the basic concepts such as the Yang-Baxter equation, commuting currents, and the algebraic Bethe ansatz. Quite extensively…
We introduce a new concept of quasi-Yang-Baxter algebras. The quantum quasi-Yang-Baxter algebras being simple but non-trivial deformations of ordinary algebras of monodromy matrices realize a new type of quantum dynamical symmetries and…
We present a nested algebraic Bethe ansatz for a one dimensional open spin chain whose boundary quantum spaces are irreducible $\mathfrak{so}_{2n}$- or $\mathfrak{sp}_{2n}$-representations and the monodromy matrix satisfies the defining…
We show how to derive exact boundary $S$ matrices for integrable quantum field theories in 1+1 dimensions using lattice regularization. We do this calculation explicitly for the sine-Gordon model with fixed boundary conditions using the…
Generic inhomogeneous integrable XXZ chains with arbitrary spins are studied by means of the quantum separation of variables (SOV) method. Within this framework, a complete description of the spectrum (eigenvalues and eigenstates) of the…
We show how any integrable 2D QFT enjoys the existence of infinitely many non--abelian {\it conserved} charges satisfying a Yang--Baxter symmetry algebra. These charges are generated by quantum monodromy operators and provide a…
A free boson on a lattice is the simplest field theory one can think of. Its partition function can be easily computed in momentum space. However, this straightforward solution hides its integrability properties. Here, we use the methods of…