Continuous representations of scalar products of Bethe vectors

TL;DR

This paper introduces continuous determinantal formulas for scalar products of Bethe vectors in the six-vertex model, applicable to both twisted and open boundary conditions, facilitating analytical and computational studies.

Contribution

It provides new families of determinantal representations parameterized by a continuous variable for scalar products of Bethe vectors in integrable models.

Findings

Families of determinantal representations derived

Applicable to models with boundary twists and open boundaries

Parameterization by a continuous complex variable

Abstract

We present families of single determinantal representations of on-shell scalar products of Bethe vectors. Our families of representations are parameterized by a continuous complex variable which can be fixed at convenience. Here we consider Bethe vectors in two versions of the six-vertex model: the case with boundary twists and the case with open boundaries.