On a long range variant of the discrete NLS equation and algebraic Bethe ansatz

We have constructed a new Quantum Nonlinear Schrodinger type periodic chain in which the interaction is long-range and not the usual nearest neighbour one. Using a new form of the transfer matrix with inhomogeneities at the lattice sites a long range Hamiltonian and its eigenvalues are extracted by using the algebraic Bethe ansatz.