Related papers: The Sine-Gordon model revisited I
The periodic $Z_n$-Belavin model on a lattice with an arbitrary number of sites $N$ is studied via the off-diagonal Bethe Ansatz method (ODBA). The eigenvalues of the corresponding transfer matrix are given in terms of an unified…
The graded off-diagonal Bethe ansatz method is proposed to study supersymmetric quantum integrable models (i.e., quantum integrable models associated with superalgebras). As an example, the exact solutions of the $SU(2|2)$ vertex model with…
Establishing the completeness of a Bethe Ansatz solution for an exactly solved model is a perennial challenge, which is typically approached on a case by case basis. For the rational, spin-1/2 Richardson--Gaudin system it will be argued…
The $A_{n-1}$ Gaudin model with integerable boundaries specified by non-diagonal K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues and the corresponding…
In this work we construct the eigenstates of the most general spin-1/2 Richardson-Gaudin model integrable in an external magnetic field. This includes the possibility for fully anisotropic XYZ coupling such that the $S^x_iS^x_j$,…
The XXZ Gaudin model with {\it generic} integerable boundaries specified by generic {\it non-diagonal} K-matrices is studied. The commuting families of Gaudin operators are diagonalized by the algebraic Bethe ansatz method. The eigenvalues…
Our goal is to develop a more general scheme for constructing integrable lattice regularisations of integrable quantum field theories. Considering the affine Toda theories as examples, we show how to construct such lattice regularisations…
We study the integrable two-site states of the quantum integrable models solvable by the nested algebraic Bethe ansatz and possessing $\mathfrak{gl}(N)$-invariant R-matrix. We investigate the overlaps between the integrable two-site states…
The construction of analytic solutions for quasi-exactly solvable systems is an interesting problem. We revisit a class of models for which the odd solutions were largely missed previously in the literature: the anharmonic oscillator, the…
We study the sine-Gordon (SG) model at finite densities of the topological charge and small SG interaction constant, related to the one-dimensional Hubbard model near half-filling. Using the modified WKB approach, we find that the spectrum…
A simple formulation of an exactly integrable $q$-oscillator model on two dimensional lattice (in 2+1 dimensional space-time) is given. Its interpretation in the terms of 2d quantum inverse scattering method and nested Bethe Ansatz…
The semiclassical limit of the algebraic Bethe Ansatz for the Izergin-Korepin 19-vertex model is used to solve the theory of Gaudin models associated with the twisted $A_{2}^{(2)}$ R-matrix. We find the spectra and eigenvectors of the $N-1$…
In this work, we generalize the numerical approach to Gaudin models developed earlier by us to degenerate systems showing that their treatment is surprisingly convenient from a numerical point of view. In fact, high degeneracies not only…
A new hidden symmetry is exhibited in the reflection equation and related quantum integrable models. It is generated by a dual pair of operators $\{\textsf{A}, \textsf{A}^*\}\in{\cal A}$ subject to $q-$deformed Dolan-Grady relations. Using…
The ground state energy of the sinh-Gordon model defined on the strip is studied using the boundary thermodynamic Bethe ansatz equation. Its ultraviolet (small width of the strip) behavior is compared with the one obtained from the boundary…
We examine the question of the integrability of the recently defined $\mathbb{Z}_2\times \mathbb{Z}_2$-graded sine-Gordon model, which is a natural generalisation of the supersymmetric sine-Gordon equation. We do this via appropriate…
We consider integrable open--boundary conditions for the supersymmetric t--J model commuting with the number operator $n$ and $S^{z}$. Four families, each one depending on two arbitrary parameters, are found. We find the relation between…
We have constructed a one dimensional exactly solvable model, which is based on the t-J model of strongly correlated electrons, but which has additional quantum group symmetry, ensuring the degeneration of states. We use Bethe Ansatz…
We solve the RSOS($p$) models on the light--cone lattice with fixed boundary conditions by disentangling the type II representations of $SU(2)_q$, at $q=e^{i\pi/p}$, from the full SOS spectrum obtained through Algebraic Bethe Ansatz. The…
We study a family of classical solutions of modified sinh-Gordon equation, $\partial_z\partial_{{\bar z}} \eta-\re^{2\eta}+p(z)\,p({\bar z})\ \re^{-2\eta}=0$ with $p(z)=z^{2\alpha}-s^{2\alpha}$. We show that certain connection coefficients…