Mass gap in the 2D O(3) nonlinear sigma model with a θ = π term

By analytic continuation to real theta of data obtained from numerical simulation at imaginary theta we study the Haldane conjecture and show that the O(3) nonlinear sigma model with a theta term in two dimensions becomes massless at theta = 3.10(5). A modified cluster algorithm has been introduced to simulate the model with imaginary theta. Two different definitions of the topological charge on the lattice have been used; one of them needs renormalization to match the continuum operator. Our work also offers a successful test for numerical methods based on analytic continuation.