  We discuss the effects of fixing the winding number in quantum Monte Carlo
simulations. We present a simple geometrical argument as well as strong
numerical evidence that one can obtain exact ground state results for periodic
boundary conditions without changing the winding number. However, for very
small systems the temperature has to be considerably lower than in simulations
with fluctuating winding numbers. The relative deviation of a calculated
observable from the exact ground state result typically scales as $T^{\gamma}$,
where the exponent $\gamma$ is model and observable dependent and the prefactor
decreases with increasing system size. Analytic results for a quantum rotor
model further support our claim.
