First principle approach to correlation functions of spin-1/2 Heisenberg chain : fourth-neighbor correlators

TL;DR

This paper develops a method using the quantum Knizhnik-Zamolodchikov equation to explicitly calculate correlation functions in the antiferromagnetic spin-1/2 Heisenberg chain, including the fourth-neighbor correlator.

Contribution

It introduces a novel approach to derive explicit correlation functions in the Heisenberg chain using fundamental relations from qKZ equations, fixing their form uniquely.

Findings

Derived all five-site correlation functions.

Obtained the analytic form of the fourth-neighbor correlator.

Validated the method by explicit calculations.

Abstract

We show how correlation functions of the spin-1/2 Heisenberg chain without magnetic field in the anti-ferromagnetic ground state can be explicitly calculated using information contained in the quantum Knizhnik-Zamolodchikov equation [qKZ]. We find several fundamental relations which the inhomogeneous correlations should fulfill. On the other hand, it turns out that these relations can fix the form of the correlations uniquely. Actually, applying this idea, we have obtained all the correlation functions on five sites. Particularly by taking the homogeneous limit, we have got the analytic form of the fourth-neighbor pair correlator < S_j^z S_{j+4}^z >.