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

Resumo

Abstract: 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.