Bethe states for the two-site Bose–Hubbard model: A binomial approach

We calculate explicitly the Bethe vectors states by the algebraic Bethe ansatz method with the gl(2)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.