Testing Haldane's Conjecture in the O(3) Model by a Meron Cluster Simulation

Twelve years ago, Haldane formulated his famous conjecture for 1-d antiferromagnetic quantum spin chains. In the context of the 2-d O(3) σ model with a θ term, it predicts a phase transition as θ → π, which has not yet been verified reliably. To simulate this we use the Wolff cluster algorithm together with an improved estimator for the charge distribution. Each cluster carries integer or half integer charge. Clusters with charge 1/2 are identified with merons. At θ = π they are inactive, such that the mass gap vanishes. We obtain critical exponents which are consistent with predictions from the k = 1 WZNW model, therefore confirming a second order phase transition.