Topological susceptibility from slabs

Abstract

In quantum field theories with topological sectors, a non-perturbative quantity of interest is the topological susceptibility χ t. In principle it seems straightforward to measure χ t by means of Monte Carlo simulations. However, for local update algorithms and fine lattice spacings, this tends to be difficult, since the Monte Carlo history rarely changes the topological sector. Here we test a method to measure χ t even if data from only one sector are available. It is based on the topological charges in sub-volumes, which we denote as slabs. Assuming a Gaussian distribution of these charges, this method enables the evaluation of χ t, as we demonstrate with numerical results for non-linear σ-models.