  We introduce a new numerical technique -- bosonic auxiliary-field Monte Carlo
(bAFMC) -- which allows to calculate the thermal properties of large
lattice-boson systems within a systematically improvable semiclassical
approach, and which is virtually applicable to any bosonic model. Our method
amounts to a decomposition of the lattice into clusters, and to an Ansatz for
the density matrix of the system in the form of a cluster-separable state --
with non-entangled, yet classically correlated clusters. This approximation
eliminates any sign problem, and can be systematically improved upon by using
clusters of growing size. Extrapolation in the cluster size allows to reproduce
numerically exact results for the superfluid transition of hardcore bosons on
the square lattice, and to provide a solid quantitative prediction for the
superfluid and chiral transition of hardcore bosons on the frustrated
triangular lattice.
