相关论文: Classification of three-state Hamiltonians solvabl…

We review some of the strategies that can be implemented to infer an $R$-matrix from the knowledge of its Hamiltonian. We apply them to the classification achieved in arXiv:1306.6303, on three state $U(1)$-invariant Hamiltonians solvable by…

The procedure for obtaining integrable open spin chain Hamiltonians via reflection matrices is explicitly carried out for some three-state vertex models. We have considered the 19-vertex models of Zamolodchikov-Fateev and Izergin-Korepin,…

Using the nested coordinate Bethe ansatz, we study 33-vertex models, where only one global charge with degenerate eigenvalues exists and each site possesses three internal degrees of freedom. In the context of Markovian processes, they…

We propose the new family of the exactly solvable discrete state BCS - type Hamiltonians based on its relationship to the six-vertex model in the quasiclassical limit both in the rational and the trigonometric cases. We establish the…

The Hamiltonian derived by Bartels, Kwiecinski and Praszalowicz for the study of high-energy QCD in the generalized logarithmic approximation was found to correspond to the Hamiltonian of an integrable $XXX$ spin chain. We study the odderon…

The nineteen-vertex models of Zamolodchikov-Fateev, Izergin-Korepin and the supersymmetric osp(1|2) with periodic boundary conditions are studied. We find the spectrum of these quantum spin chains using the Coordinate Bethe Ansatz. The…

Three well-known solutions of the Gaudin equation are obtained under a set of standard assumptions. By relaxing one of these assumptions we introduce a class of mutually commuting Hamiltonians based on a different solution of the Gaudin…

We compute the eigenfunctions and eigenvalues of the periodic integrable spin s XXX model using the coordinate Bethe ansatz. To do so, we compute explicitly the Hamiltonian of the model. These results generalize what has been obtained for…

The Coordinate Bethe Ansatz (CBA) expresses, as a sum over permutations, the matrix element of an XXX Heisenberg spin chain Hamiltonian eigenstate with a state with fixed spins. These matrix elements comprise the wave functions of the…

New exactly solvable nineteen vertex models and related quantum spin-1 chains are solved. Partition functions, excitation energies, correlation lengths, and critical exponents are calculated. It is argued that one of the non-critical…

We define one-dimensional particles with generalized exchange statistics. The exact solution of a Hubbard-type Hamiltonian constructed with such particles is achieved using the Coordinate Bethe Ansatz. The chosen deformation of the…

The integrable open-boundary conditions for the Bariev model of three coupled one-dimensional XY spin chains are studied in the framework of the boundary quantum inverse scattering method. Three kinds of diagonal boundary K-matrices leading…

The Bethe ansatz in its several formulations is the common tool for the exact solution of one dimensional quantum Hamiltonians. This ansatz asserts that the several eigenfunctions of the Hamiltonians are given in terms of a sum of…

We examine the question of whether Bethe's ansatz reproduces all states in the periodic Heisenberg XXZ and XXX spin chains. As was known to Bethe himself, there are states for which the Bethe momenta $k_n$ diverge: these are in fact the…

We consider systems where dynamical variables are the generators of the SU(2) group. A subset of these Hamiltonians is exactly solvable using the Bethe ansatz techniques. We show that Bethe ansatz equations are equivalent to polynomial…

We investigate symmetry properties of the Bethe ansatz wave functions for the Heisenberg $XXZ$ spin chain. The $XXZ$ Hamiltonian commutes simultaneously with the shift operator $T$ and the lattice inversion operator $V$ in the space of…

It is shown that solutions of the Bethe ansatz equations for the inhomogeneous arbitrary spin XXX or XXZ model satisfy certain identites which generalize those, recently obtained by K.Fabricius and B.M.McCoy, for solutions of the Bethe…

By means of an algebraic Bethe ansatz approach we study the Zamolodchikov-Fateev and Izergin-Korepin vertex models with non-diagonal boundaries, characterized by reflection matrices with an upper triangular form. Generalized Bethe vectors…

We work out finite-dimensional integral formulae for the scalar product of genus one states of the group $G$ Chern-Simons theory with insertions of Wilson lines. Assuming convergence of the integrals, we show that unitarity of the elliptic…

We find an analytic solution of the Bethe Ansatz equations (BAE) for the special case of a finite XXZ spin chain with free boundary conditions and with a complex surface field which provides for $U_q(sl(2))$ symmetry of the Hamiltonian.…