# Why scalar products in the algebraic Bethe ansatz have determinant representation

## TL;DR

This paper demonstrates that scalar products in algebraic Bethe ansatz models can be characterized by linear equations, providing solutions for various models including the XXX spin chain with broken symmetry.

## Contribution

It introduces a novel linear equation framework for scalar products in algebraic Bethe ansatz, extending to models with broken symmetry.

## Key findings

- Scalar products satisfy a system of linear equations
- Solutions found for a wide class of integrable models
- Applied method to XXX spin chain with broken U(1) symmetry

## Abstract

We show that the scalar products of on-shell and off-shell Bethe vectors in the algebra1ic Bethe ansatz solvable models satisfy a system of linear equations. We find solutions to this system for a wide class of integrable models. We also apply our method to the XXX spin chain with broken $U(1)$ symmetry.