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

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

1995-05-26

arxiv.org/abs/cond-mat/9505132v1

Phys. Rev. B 52, R719 (1995)

Physics

Condensed Matter

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

Scientific paper

10.1103/PhysRevB.52.R719

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 $g_{eff}(l_0)=1/\ln(cl_0)$, as predicted by field theoretical treatments.

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