On the algebraic Bethe Ansatz approach to the correlation functions of the XXZ spin-1/2 Heisenberg chain

TL;DR

This paper reviews an algebraic Bethe Ansatz method for calculating correlation functions in the XXZ spin-1/2 Heisenberg chain, linking multiple integral representations with form factor expansions.

Contribution

It introduces a unified approach to compute correlation functions using algebraic Bethe Ansatz, simplifying existing formulas and connecting different representations.

Findings

Finite chain two-point functions expressed as a single multiple integral

Established a direct link between multiple integral formulas and form factor expansions

Provided a comprehensive review of the algebraic Bethe Ansatz method for correlation functions

Abstract

We present a review of the method we have elaborated to compute the correlation functions of the XXZ spin-1/2 Heisenberg chain. This method is based on the resolution of the quantum inverse scattering problem in the algebraic Bethe Ansatz framework, and leads to a multiple integral representation of the dynamical correlation functions. We describe in particular some recent advances concerning the two-point functions: in the finite chain, they can be expressed in terms of a single multiple integral. Such a formula provides a direct analytic connection between the previously obtained multiple integral representations and the form factor expansions for the correlation functions.