Numerical evidence for multiplicative logarithmic corrections from marginal operators

Field theory calculations predict multiplicative logarithmic corrections to correlation functions from marginally irrelevant operators. However, for the numerically most suitable model, the spin-½ chain, these corrections have been controversial. In this paper, the spin-spin correlation function of the antiferromagnetic spin-½ chain is calculated numerically in the presence of a next-nearest-neighbor coupling $J_2$ for chains of up to 32 sites. By varying the coupling strength $J_2$ 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 $\frac{J_2}{J}=0.241167\mathrm{}\pm 0.000005$.