Finite-size scaling for the S=1/2 Heisenberg Antiferromagnetic Chain

TL;DR

This paper calculates sub-leading logarithmic corrections to the finite-size correlation function in the S=1/2 Heisenberg antiferromagnetic chain using renormalization group methods, improving agreement with numerical data.

Contribution

It introduces a detailed calculation of logarithmic corrections to correlation functions, enhancing understanding of finite-size effects in quantum spin chains.

Findings

Logarithmic corrections decay slowly with chain size

Renormalization group improves theoretical predictions

Better alignment with numerical results achieved

Abstract

Corrections to the asymptotic correlation function in a Heisenberg spin-1/2 antiferromagnetic spin chain are known to vanish slowly (logarithmically) as a function of the distance r or the chain size L. This leads to significant differences with numerical results. We calculate the sub-leading logarithmic corrections to the finite-size correlation function, using renormalization group improved perturbation theory, and compare the result with numerical data.