Correlation Function of the Spin-1/2 XXX Antiferromagnet

TL;DR

This paper investigates a specific correlation function in the spin-1/2 XXX antiferromagnet, providing exact representations that are effective for analyzing both short and long distance behaviors in the ground state.

Contribution

It introduces two exact representations of the correlation function, optimized for different distance regimes, advancing analytical understanding of the model.

Findings

Exact representations for the correlation function at any distance.

One representation is more effective for long-distance analysis.

The other is optimized for short-distance behavior.

Abstract

We consider a special correlation function in the isotropic spin-$\half$ Heisenberg antiferromagnet. It is the probability of finding a ferromagnetic string of (adjacent) spins in the antiferromagnetic ground state. We give two different representations for this correlation function. Both of them are exact at any distance, but one becomes more effective for the description of long distance behaviour, the other for the description of short distance behaviour.