Correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field

TL;DR

This paper derives multiple integral formulas for the correlation functions of the XXZ Heisenberg spin-1/2 chain in a magnetic field using algebraic Bethe ansatz, connecting with known results in special cases.

Contribution

It provides a unified integral representation of correlation functions for the XXZ chain in a magnetic field, extending previous results to include magnetic effects.

Findings

Integral representations valid in both massless and massive regimes.

Consistency with known results at zero magnetic field.

Connection with quantum affine algebra and corner transfer matrix methods.

Abstract

Using the algebraic Bethe ansatz method, and the solution of the quantum inverse scattering problem for local spins, we obtain multiple integral representations of the $n$-point correlation functions of the XXZ Heisenberg spin-$1 \over 2$ chain in a constant magnetic field. For zero magnetic field, this result agrees, in both the massless and massive (anti-ferromagnetic) regimes, with the one obtained from the q-deformed KZ equations (massless regime) and the representation theory of the quantum affine algebra ${\cal U}_q (\hat{sl}_2)$ together with the corner transfer matrix approach (massive regime).