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

Abstract

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${)}^{\mathit{l}}$\ensuremath{\omega}(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 \ensuremath{\omega}(l,N)=\ensuremath{\omega}(l,\ensuremath{\infty})${\mathit{f}}_{\mathit{XY}}^{\mathrm{\ensuremath{\alpha}}}$(l/N) proposed by Kaplan et al., which is used to determine \ensuremath{\omega}(l,\ensuremath{\infty}). The asymptotic correlation function \ensuremath{\omega}(l,\ensuremath{\infty}) and the magnetic structure factor S(q=\ensuremath{\pi}) show logarithmic corrections consistent with \ensuremath{\omega}(l,\ensuremath{\infty})\ensuremath{\sim}a\ensuremath{\surd}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.