Scalar product of Bethe vectors from functional equations

TL;DR

This paper investigates the scalar product of Bethe vectors in the six-vertex model using functional equations derived from the Yang-Baxter algebra, providing a solution expressed as a multiple contour integral.

Contribution

It introduces a novel approach to compute scalar products of Bethe vectors via functional equations and offers an explicit integral representation of the solution.

Findings

Scalar products obey a system of functional equations

Solution expressed as a multiple contour integral

Method based on Yang-Baxter algebra

Abstract

In this work the scalar product of Bethe vectors for the six-vertex model is studied by means of functional equations. The scalar products are shown to obey a system of functional equations originated from the Yang-Baxter algebra and its solution is given as a multiple contour integral.