Numerical Evidence for Multiplicative Logarithmic Corrections from Marginal Operators

TL;DR

This study numerically confirms field theory predictions of multiplicative logarithmic corrections in the spin-1/2 chain, identifying the precise coupling where the marginal operator's effect vanishes.

Contribution

The paper provides the first clear numerical evidence supporting theoretical predictions of logarithmic corrections from marginal operators in the spin-1/2 chain.

Findings

Confirmed the presence of multiplicative logarithmic corrections

Determined the critical coupling J2 where the marginal operator vanishes

Validated field theory predictions through numerical analysis

Abstract

Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model - the spin-1/2 chain - these corrections have been controversial. In this paper, the spin-spin correlation function of the antiferromagnetic spin-1/2 chain is calculated numerically in the presence of a next nearest neighbor coupling J2 for chains of up to 32 sites. By varying the coupling strength J2 we can control the effect of the marginal operator, and our results unambiguously confirm the field theory predictions. The critical value at which the marginal operator vanishes has been determined to be at J2 = 0.241167 +/- 0.000005J.