Spin-correlation function of the S=1 antiferromagnetic Heisenberg chain at T=0

The correlation function ρ(l)=<S^z_iS^z_i+l> is calculated for the spin-1 Heisenberg antiferromagnetic chain (H=JΣ_iscrS_iscrS_i+1, scrS_N+1≡scrS₁) 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 ⁴He.