We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)-invariant R-matrix for the two-site Bose–Hubbard model. Using a binomial expansion of the n-th power of a sum of two operators we get and solve a recursion equation. We calculate the scalar product and the norm of the Bethe vectors states. The form factors of the imbalance current operator are also computed.
Physics letters. B. Vol. 746 (June 2015), p. 186-189