We introduce a new numerical technique -- bosonic auxiliary-field Monte Carlo(bAFMC) -- which allows to calculate the thermal properties of largelattice-boson systems within a systematically improvable semiclassicalapproach, and which is virtually applicable to any bosonic model. Our methodamounts to a decomposition of the lattice into clusters, and to an Ansatz forthe density matrix of the system in the form of a cluster-separable state --with non-entangled, yet classically correlated clusters. This approximationeliminates any sign problem, and can be systematically improved upon by usingclusters of growing size. Extrapolation in the cluster size allows to reproducenumerically exact results for the superfluid transition of hardcore bosons onthe square lattice, and to provide a solid quantitative prediction for thesuperfluid and chiral transition of hardcore bosons on the frustratedtriangular lattice.
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