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The correlation function (l) =〈S₈^zS₈+₋^z〉 is calculated for the spin-1 Heisenberg antiferromagnetic chain (H=J₈scrS₈scrS₈+₁, scrS₍+₁scrS₁) at the ground state. Using the Monte Carlo method of Hirsch, Sugar, Scalopino, and Blankenbecler we find that (l) decays exponentially in contrast to the S=half case where (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.
Minoru Takahashi (Thu,) studied this question.