General scalar products in the arbitrary six-vertex model

TL;DR

This paper derives a general scalar product formula for the six-vertex model with arbitrary weights using algebraic Bethe ansatz, unitarity, and Yang-Baxter algebra, providing explicit expressions for generic Boltzmann weights.

Contribution

It introduces a new explicit formula for the scalar product in the six-vertex model with arbitrary weights, expanding the analytical tools available for integrable models.

Findings

Derived a recurrence relation for the scalar product

Expressed scalar product in terms of domain wall partition functions

Obtained explicit formulas for generic Boltzmann weights

Abstract

In this work we use the algebraic Bethe ansatz to derive the general scalar product in the six-vertex model for generic Boltzmann weights. We performed this calculation using only the unitarity property, the Yang-Baxter algebra and the Yang-Baxter equation. We have derived a recurrence relation for the scalar product. The solution of this relation was written in terms of the domain wall partition functions. By its turn, these partition functions were also obtained for generic Boltzmann weights, which provided us with an explicit expression for the general scalar product.