Recursive formulas for the overlaps between Bethe states and product states in XXZ Heisenberg chains

Abstract: We consider the problem of computing the overlaps between the Bethe states of the XXZ spin-1/2 chain and generic states. We derive recursive formulas for the overlaps between some simple product states and off-shell Bethe states within the framework of the Algebraic Bethe Ansatz. These recursive formulas can be used to prove in a simple and straightforward way the recently-obtained results for the overlaps of the Bethe states with the N\'eel state, the dimer state, and the \textit{q}-deformed dimer state. However, these recursive formulas are derived for a broader class of states and represent a concrete starting point for the computation of rather general overlaps. Our approach can be easily extended to other one-dimensional Bethe Ansatz integrable models.