Slavnov and Gaudin-Korepin Formulas for Models without ${\rm U}(1)$ Symmetry: the Twisted XXX Chain

TL;DR

This paper derives modified Slavnov and Gaudin-Korepin formulas for the spectral problem of the twisted XXX spin-1/2 Heisenberg chain, a quantum integrable model lacking ${ m U}(1)$ symmetry, using a modified algebraic Bethe ansatz.

Contribution

It provides the first explicit formulas for scalar products in models without ${ m U}(1)$ symmetry, expanding the algebraic Bethe ansatz framework.

Findings

Derived modified Slavnov formula for the twisted XXX chain

Obtained Gaudin-Korepin formula for the model

First example of such formulas for non-${ m U}(1)$ symmetric models

Abstract

We consider the XXX spin-$\frac{1}{2}$ Heisenberg chain on the circle with an arbitrary twist. We characterize its spectral problem using the modified algebraic Bethe anstaz and study the scalar product between the Bethe vector and its dual. We obtain modified Slavnov and Gaudin-Korepin formulas for the model. Thus we provide a first example of such formulas for quantum integrable models without ${\rm U}(1)$ symmetry characterized by an inhomogenous Baxter T-Q equation.