XX and Ising limits in integral formulae for finite temperature correlation functions of the XXZ chain

TL;DR

This paper derives simplified integral formulas for finite temperature correlation functions of the XXZ chain in the XX and Ising limits, connecting known results through reduction of multiple integrals to single integrals.

Contribution

It provides a unified integral representation approach that simplifies the calculation of finite temperature correlations in the XX and Ising limits of the XXZ chain.

Findings

Multiple integrals reduce to single integrals in the XX and Ising limits.

Reproduction of known correlation function results in these limits.

Provides a bridge between integral representations and known analytical solutions.

Abstract

We consider a multiple integral representation for a one-parameter generating function of the finite temperature $S^z$-$S^z$ correlation functions of the antiferromagnetic spin-1/2 XXZ chain in the XX limit and in the Ising limit. We show how in these limits the multiple integrals reduce to single integrals, thereby reproducing known results.