  Path integrals are usually formulated in discrete Euclidean time using the
Trotter formula. We propose a new method to study discrete quantum systems, in
which we work directly in the Euclidean time continuum. The method is of
general interest and can be applied to studies of quantum spin systems, lattice
fermions, and in principle also lattice gauge theories. Here it is applied to
the Heisenberg quantum antiferromagnet using a continuous-time version of a
loop cluster algorithm. The computational advantage of this algorithm is
exploited to confirm the predictions of chiral perturbation theory in the
extreme low temperature regime, down to $T = 0.01 J$. A fit of the low-energy
parameters of chiral perturbation theory gives excellent agreement with
previous results and with experiments.
