Numerical Evidence for the Haldane Conjecture

Abstract

The Haldane conjecture, when applied to the Heisenberg O(3) model with a θ term in two dimensions, states that the correlation length diverges when θ approaches π. To verify this conjecture we have numerically simulated the model at imaginary θ and then analytically continued the results to real θ. We have obtained that the value where the model should become critical is θ=3.10(5) in agreement with the expectation.

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