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 applied here to the Heisenberg quantum antiferromagnet usin
g a continuous-time version of a loop cluster algorithm. This algorith
m is exploited to confirm the predictions of chiral perturbation theor
y in the extreme low temperature regime, down to T = 0.01J. A fit of t
he low-energy parameters of chiral perturbation theory gives excellent
agreement with previous results and with experiments.