Fifth-neighbor spin-spin correlator for the anti-ferromagnetic Heisenberg chain

TL;DR

This paper derives explicit formulas for the fifth-neighbor spin-spin correlator in the anti-ferromagnetic Heisenberg chain using functional relations from the quantum Knizhnik-Zamolodchikov equation, extending previous calculations.

Contribution

It introduces a method to compute higher-order spin correlators in the Heisenberg chain via functional relations, providing explicit results up to the fifth neighbor.

Findings

Explicit form of generating functions up to n=6

Correlator <S_j^z S_{j+5}^z> computed

Functional relations derived from quantum KZ equation

Abstract

We study the generating function of the spin-spin correlation functions in the ground state of the anti-ferromagnetic spin-1/2 Heisenberg chain without magnetic field. We have found its fundamental functional relations from those for general correlation functions, which originate in the quantum Knizhink-Zamolodchikov equation. Using these relations, we have calculated the explicit form of the generating functions up to n=6. Accordingly we could obtain the spin-spin correlator <S_j^z S_{j+k}^z> up to k=5.