Exact results for the sigma^z two-point function of the XXZ chain at Delta=1/2

TL;DR

This paper derives exact multiple integral formulas for the z-z correlation function in the XXZ spin chain at Delta=1/2, enabling explicit computation of these correlations for distances up to 8.

Contribution

It introduces a new integral representation that can be separated and computed exactly at Delta=1/2, providing explicit correlation values.

Findings

Exact integral formulas for the correlation function at Delta=1/2

Explicit results for lattice distances up to 8

Correlation values are rational numbers divided by powers of 2

Abstract

We propose a new multiple integral representation for the correlation function <sigma_1^z sigma_{m+1}^z> of the XXZ spin-1/2 Heisenberg chain in the disordered regime. We show that for Delta=1/2 the integrals can be separated and computed exactly. As an example we give the explicit results up to the lattice distance m=8. It turns out that the answer is given as integer numbers divided by 2^[(m+1)^2].