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We propose to compute physical properties by Monte Carlo calculations usingconditional expectation values. The latter are obtained on top of the usualMonte Carlo sampling by partitioning the physical space in several subspaces orfragments, and subsampling each fragment (i.e., performing side walks) whilefreezing the environment. No bias is introduced and a zero-variance principleholds in the limit of separability, i.e. when the fragments are independent. Inpractice, the usual bottleneck of Monte Carlo calculations -- the scaling ofthe statistical fluctuations as a function of the number of particles N -- isrelieved for extensive observables. We illustrate the method in variationalMonte Carlo on the 2D Hubbard model and on metallic hydrogen chains usingJastrow-Slater wave functions. A factor O(N) is gained in numerical efficiency.

Systematic lowering of the scaling of Monte Carlo calculations by partitioning andsubsampling