Interpreting numerical measurements in fixed topological sectors

Abstract

For quantum field theories with topological sectors, Monte Carlo simulations on fine lattices tend to be obstructed by an extremely long autocorrelation time with respect to the topological charge. Then reliable numerical measurements are feasible only within individual sectors. The challenge is to assemble such restricted measurements in a way that leads to a substantiated approximation to the fully fledged result, which corresponds to the correct sampling over the entire set of configurations. We test an approach for such a topological summation, which was suggested by Brower, Chandrasekharan, Negele and Wiese. Under suitable conditions, energy levels and susceptibilities can be obtained to a good accuracy, as we demonstrate for $\mathrm{O}(N)$ models, SU(2) Yang-Mills theory, and for the Schwinger model.