A simulation of the Schwinger model in the overlap formalism

Abstract

In the continuum, the single flavor massless Schwinger model has an exact global axial U(1) symmetry in the sector of perturbative gauge fields. This symmetry is explicitly broken by gauge fields with nonzero topological charge inducing a nonzero expectation value for the bilinear ψ ψ. We show that a lattice formulation of this model, using the overlap formalism to treat the massless fermions, explicitly exhibits this phenomenon. A Monte Carlo simulation of the complete system yields the correct value of the fermion condensate and shows unambiguously that it originates from the sector of topological charge equal to unity.