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

TL;DR

This paper explicitly constructs Bethe vectors for the two-site Bose-Hubbard model using algebraic Bethe ansatz, deriving formulas for scalar products, norms, and form factors, advancing analytical understanding of the model.

Contribution

It introduces a binomial expansion approach to explicitly calculate Bethe vectors and related quantities for the two-site Bose-Hubbard model.

Findings

Explicit Bethe vectors are constructed for the model.

Scalar products and norms of Bethe states are derived.

Form factors of the imbalance current operator are computed.

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.