Off-shell scalar products for the $XXZ$ spin chain with open boundaries

TL;DR

This paper derives a multiple contour integral representation for scalar products of Bethe vectors in the open boundary $XXZ$ spin chain, facilitating easier computation of these quantities.

Contribution

It introduces a novel functional equation approach to express scalar products as solutions within the reflection algebra framework.

Findings

Derived a multiple contour integral formula for scalar products

Simplified the homogeneous limit calculation

Provided a new functional relation-based method

Abstract

In this work we study scalar products of Bethe vectors associated with the $XXZ$ spin chain with open boundary conditions. The scalar products are obtained as solutions of a system of functional equations. The description of scalar products through functional relations follows from a particular map having the reflection algebra as its domain and a function space as the codomain. Within this approach we find a multiple contour integral representation for the scalar products in which the homogeneous limit can be obtained trivially.