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.
Highlights
The first experimental verification of the Bose–Einstein condensation (BEC) [1,2,3] occurred after a gap of more than seven decades following its theoretical prediction [4,5]
In this direction the quantum inverse scattering method (QISM) [14,15,16,17,18] has been used to solve and study some prototypical many-body models that contribute to describe phenomena associated to BEC [19,20,21]
We develop and use a new method to explicitly calculate the Bethe vectors states (BVS) and obtain the scalar product of two BVS for the two-site Bose–Hubbard model
Summary
The first experimental verification of the Bose–Einstein condensation (BEC) [1,2,3] occurred after a gap of more than seven decades following its theoretical prediction [4,5]. A fruitful instrument in relation to ultracold physics are many-body atomic models related to BEC In this direction the quantum inverse scattering method (QISM) [14,15,16,17,18] has been used to solve and study some prototypical many-body models that contribute to describe phenomena associated to BEC [19,20,21]. Another important application is in the calculation of the average values of the operators as for example correlation operators. Applying this method, some physical quantities for the Hamiltonian (1) were obtained in [38]. As an application we obtain the form factors (non-normalized) for the imbalance current operator
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