We consider a trial wave function for the two-dimensional spin-{} antiferromagnetic Heisenberg model (resonating-valence-bond state), which is a sum of all dimerizations. It is shown that the antiferromagnetic correlation length is bounded by that of a classical gas of interacting loops with $n=4$ components. We argue that the range of the antiferromagnetic correlations is finite and triplet excitation has an energy gap.
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Kohmoto et al. (1988) studied this question.
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