Numerical renormalization group study of the correlation functions of the antiferromagnetic spin-$\frac{1}{2}$ Heisenberg chain

Abstract

We use the density-matrix renormalization group technique developed by White \cite{white} to calculate the spin correlation functions $<S_{n+l}^z{S}_n^z>=(-1{)}^l\omega (l,N)$ for isotropic Heisenberg rings up to $N=70$ sites. The correlation functions for large $l$ and $N$ are found to obey the scaling relation $\omega (l,N)=\omega (l,\infty )f_{XY}^{\alpha }(l/N)$ proposed by Kaplan et al. \cite{horsch} , which is used to determine $\omega (l,\infty )$. The asymptotic correlation function $\omega (l,\infty )$ and the magnetic structure factor $S(q=\pi )$ show logarithmic corrections consistent with $\omega (l,\infty )\sim a\sqrt{\ln cl}/l$, where $c$ is related to the cut-off dependent coupling constant $g_{eff}(l_0)=1/\ln (c{l}_0)$, as predicted by field theoretical treatments.

Accepted in Phys. Rev. B. 4 pages of text in Latex + 5 figures in uuencoded form containing the 5 postscripts (mailed separately)