We propose a new method to study path integrals for discrete quantum s
ystems in which we work directly in the Euclidean time continuum. The
method is of general interest. Here it is applied to the Heisenberg qu
antum antiferromagnet using a continuous-time version of a loop cluste
r algorithm. This algorithm is exploited to confirm the predictions of
chiral perturbation theory in the extreme low temperature regime, dow
n to T = 0.01J. A fit of the low-energy parameters of chiral perturbat
ion theory gives excellent agreement with previous results and with ex
periments.