Related papers: Algebraic Bethe Ans\"atze and eigenvalue-based det…
We present a novel approach for computing reduced density matrices for superpositions of eigenstates of a Bethe-ansatz solvable model by direct integration of the wave function in coordinate representation. A diagrammatic approach is…
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 introduce and study a class of two-dimensional integrable quantum field theories that carry an internal $\mathbb{Z}_n$ structure. These models extend factorised scattering beyond the conventional framework, featuring both the usual…
In the derivation of the generating function of the Gaudin Hamiltonians with boundary terms, we follow the same approach used previously in the rational case, which in turn was based on Sklyanin's method in the periodic case. Our derivation…
A new algebraic Bethe ansatz scheme is proposed to diagonalise classes of integrable models relevant to the description of Bose-Einstein condensates in dilute alkali gases. This is achieved by introducing the notion of Z-graded…
We construct the enveloping fundamental spin model of the t-J hamiltonian using the Quantum Inverse Scattering Method (QISM), and present all three possible Algebraic Bethe Ans\"atze. Two of the solutions have been previously obtained in…
We derive the Bethe Ansatz Equations on the half line for particles interacting through factorized $S$-matrices invariant relative to the centrally extended $su(2|2)$ Lie superalgebra and $su(1|2)$ open boundaries. These equations may be of…
A simple model of nucleons coupled to angular momentum zero (s-pairs) occupying the valance shell of a semi-magic nuclei is considered. The model has a separable, orbit dependent pairing interaction which dominates over the kinetic term. It…
A general graded reflection equation algebra is proposed and the corresponding boundary quantum inverse scattering method is formulated. The formalism is applicable to all boundary lattice systems where an invertible R-matrix exists. As an…
Recently a new class of quantum integrable models, the cyclotomic Gaudin models, were described in arXiv:1409.6937, arXiv:1410.7664. Motivated by these, we identify a class of affine hyperplane arrangements that we call cyclotomic…
The exact solutions of the $D^{(1)}_3$ model (or the $so(6)$ quantum spin chain) with either periodic or general integrable open boundary conditions are obtained by using the off-diagonal Bethe Ansatz. From the fusion, the complete operator…
These lecture notes are devoted to the recent progress in the geometric aspects of quantum integrable systems based on quantum groups solved using the Bethe ansatz technique. One part is devoted to their enumerative geometry realization…
The integrable XXZ alternating spin chain with generic non-diagonal boundary terms specified by the most general non-diagonal K-matrices is studied via the off-diagonal Bethe Ansatz method. Based on the intrinsic properties of the fused…
We show that the stochastic dynamics of a large class of one-dimensional interacting particle systems may be presented by integrable quantum spin Hamiltonians. Using the Bethe ansatz and similarity transformations this yields new exact…
Schr\"odinger equation for Bose gas with repulsive contact interactions in one-dimensional space may be solved analytically with the help of the Bethe ansatz if we impose periodic boundary conditions. It was shown that in such a system…
The encoding of all possible sets of Bethe equations for a spin chain with SU(N|M) symmetry into a QQ-system calls for an expression of spin chain overlaps entirely in terms of Q-functions. We take a significant step towards deriving such a…
A scheme based on a unifying q-deformed algebra and associated with a generalized Lax operator is proposed for generating integrable quantum and statistical models. As important applications we derive known as well as novel quantum models…
The semiclassical limit of the algebraic quantum inverse scattering method is used to solve the theory of the Gaudin model. Via Off-shell Bethe ansatz equations of an integrable representation of the graded osp(1|2) vertex model we find the…
Recent studies of strongly interacting atoms and photons in optical cavities have rekindled interest in the Dicke model of atomic qubits coupled to discrete photon cavity modes. We study the multimode Dicke model with variable atom-photon…
The Gaudin models based on the face-type elliptic quantum groups and the $XYZ$ Gaudin models are studied. The Gaudin model Hamiltonians are constructed and are diagonalized by using the algebraic Bethe ansatz method. The corresponding…