Scalar products in GL(3)-based models with trigonometric R-matrix. Determinant representation

TL;DR

This paper derives a determinant formula for scalar products and form factors in GL(3) integrable models with a trigonometric R-matrix, highlighting key differences from GL(3)-invariant models.

Contribution

It provides a new determinant representation for scalar products in GL(3) models with a trigonometric R-matrix, enabling explicit form factor calculations.

Findings

Determinant formula for scalar products of Bethe vectors

Explicit form factor formula for monodromy matrix entries

Identifies differences between trigonometric and GL(3)-invariant models

Abstract

We study quantum integrable GL(3)-based models with a trigonometric R-matrix solvable by the nested algebraic Bethe ansatz. We derive a determinant representation for a special case of scalar products of Bethe vectors. This representation allows one to find a determinant formula for the form factor of one of the monodromy matrix entries. We also point out essential difference between form factors in the models with the trigonometric R-matrix and their analogs in GL(3)-invariant models.