Correlation functions of the spin-1/2 anti-ferromagnetic Heisenberg chain: exact calculation via the generating function

TL;DR

This paper derives exact analytical expressions for spin-spin correlation functions in the spin-1/2 antiferromagnetic Heisenberg chain at zero temperature using generating functions, advancing understanding of quantum spin chains.

Contribution

It introduces a method to exactly calculate correlation functions via generating functions derived from quantum Knizhnik-Zamolodchikov equations, providing explicit results up to eight lattice sites.

Findings

Analytical expressions for correlation functions up to eight sites.

Numerical confirmation via exact diagonalization.

Method applicable to inhomogeneous correlation functions.

Abstract

Analytical expressions of some of the spin-spin correlation functions up to eight lattice sites for the spin-1/2 anti-ferromagnetic Heisenberg chain at zero temperature without magnetic field are obtained. The key object of our method is the generating function of two-point spin-spin correlators, whose functional relations are derived from those for general inhomogeneous correlation functions previously obtained from the quantum Knizhnik-Zamolodchikov equations. We show how the generating functions are fully determined by their functional relations, which leads to the two-point spin-spin correlators. The obtained analytical results are numerically confirmed by the exact diagonalization for finite systems.