Exact Correlation Amplitude for the S=1/2 Heisenberg Antiferromagnetic Chain

TL;DR

This paper derives the exact amplitude of the asymptotic spin correlation function in the S=1/2 Heisenberg antiferromagnetic chain, providing precise mathematical characterization of its decay behavior.

Contribution

It presents the exact amplitude for the correlation function in the S=1/2 Heisenberg antiferromagnetic chain, including analysis of anisotropy effects and finite-size corrections.

Findings

Exact amplitude of correlation function derived

Correlation decay characterized as (-1)^r (ln r)^{1/2}/r

Finite-size correction forms analyzed

Abstract

The exact amplitude for the asymptotic correlation function in the S=1/2 Heisenberg antiferromagnetic chain is determined: <S^a_0 S^b_r> goes to (-1)^r delta^{ab}(ln r)^{1/2}/[(2 pi)^{3/2}r]. The behaviour of the correlation functions for small xxz anisotropy and the form of finite-size corrections to the correlation function are also analysed.