Simulations of Discrete Quantum Systems in Continuous Euclidean Time

Abstract

We propose a new method to study path integrals for discrete quantum systems in which we work directly in the Euclidean time continuum. The method is of general interest. Here it is applied to the Heisenberg quantum antiferromagnet using a continuous-time version of a loop cluster algorithm. This algorithm is exploited to confirm the predictions of chiral perturbation theory in the extreme low temperature regime, down to $T\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0.01J$. A fit of the low-energy parameters of chiral perturbation theory gives excellent agreement with previous results and with experiments.