Measurements with topological restrictions

We address models in quantum field theory with topological sectors, and
difficulties with their Monte Carlo simulation. In particular we are
concerned with the situation where a simulation has an extremely long
auto-correlation time with respect to the topological charge. Then
reliable numerical measurements are feasible only within individual
topological sectors. The challenge is to assemble such restricted
measurements to obtain a systematic approximation for the full-fledged
result, which would correspond to the correct sampling over the entire set
of configurations. Amazingly, under certain conditions this is possible,
and it provides in addition an estimate for the topological susceptibility
chi_t. We test this scenario, and also an alternative approach to measure chi_t from the
topological charge density correlation in a fixed sector.