Long-distance asymptotics of spin-spin correlation functions for the XXZ spin chain

TL;DR

This paper analyzes the long-distance behavior of spin-spin correlations in the XXZ Heisenberg chain, using conformal field theory and exact form factor results to determine asymptotic amplitudes, including the isotropic limit.

Contribution

It provides new asymptotic expansions and correlation amplitudes for the XXZ chain by comparing form factors across related models and analyzing the isotropic limit.

Findings

Derived asymptotic expansions for spin-spin correlations.

Determined correlation amplitudes for leading and sub-leading terms.

Analyzed the isotropic (XXX) limit of the expansions.

Abstract

We study asymptotic expansions of spin-spin correlation functions for the XXZ Heisenberg chain in the critical regime. We use the fact that the long-distance effects can be described by the Gaussian conformal field theory. Comparing exact results for form factors in the XYZ and sine-Gordon models, we determine correlation amplitudes for the leading and main sub-leading terms in the asymptotic expansions of spin-spin correlation functions. We also study the isotropic (XXX) limit of these expansions.