Spin-correlation function of theS=1antiferromagnetic Heisenberg chain atT=0

The correlation function ρ(l)=〈$S_i^z$ $S_{i+l}^z$〉 is calculated for the spin-1 Heisenberg antiferromagnetic chain (H=J${\Sigma }_i$ ${\mathrm{scrS}}_i$ ${\mathrm{scrS}}_{i+1\mathrm{}}$, ${\mathrm{scrS}}_{N+1\mathrm{}}$≡${\mathrm{scrS}}_1$) at the ground state. Using the Monte Carlo method of Hirsch, Sugar, Scalopino, and Blankenbecler we find that ρ(l) decays exponentially in contrast to the S=half case where ρ(l) decays algebraically. This fact coincides with Haldane’s prediction and recent numerical calculations. We calculate the upper bound of elementary excitation from the structure factor using a variational method which resembles the Feynman theory for elementary excitation of liquid ${}_{}{}^4{}_{}{}^{}\mathrm{He}$.