Numerical renormalization-group study of the correlation functions of the antiferromagnetic spin-1/2 Heisenberg chain

We use the density-matrix renormalization-group technique developed by White to calculate the spin correlation functions 〈${\mathit{S}}_{\mathit{n}+\mathit{l}}^{\mathit{z}}$ ${\mathit{S}}_{\mathit{n}}^{\mathit{z}}$〉=(-1${)}^{\mathit{l}}$ω(l,N) for isotropic Heisenberg rings up to N=70 sites. The correlation functions for large l and N are found to obey the scaling relation ω(l,N)=ω(l,∞)${\mathit{f}}_{\mathit{XY}}^{\mathrm{\alpha }}$(l/N) proposed by Kaplan et al., which is used to determine ω(l,∞). The asymptotic correlation function ω(l,∞) and the magnetic structure factor S(q=π) show logarithmic corrections consistent with ω(l,∞)∼a√lncl /l, where c is related to the cut-off dependent coupling constant ${\mathit{g}}_{\mathrm{eff}}$(${\mathit{l}}_0$)=1/ln(${\mathit{cl}}_0$), as predicted by field theoretical treatments.