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In Monte Carlo simulations, proposed configurations are accepted or rejectedaccording to an acceptance ratio, which depends on an underlying probabilitydistribution and an a priori sampling probability. By carefully selecting theprobability distribution from which random variates are sampled, simulationscan be made more efficient, by virtue of an autocorrelation time reduction. Inthis paper, we illustrate how to directly sample random variates from a twodimensional truncated exponential distribution. We show that our directsampling approach converges faster to the target distribution compared torejection sampling. The direct sampling of one and two dimensional truncatedexponential distributions is then applied to a recent Path Integral Monte Carlo(PIMC) algorithm for the simulation of Bose-Hubbard lattice models at zerotemperature. The new sampling method results in improved acceptance ratios andreduced autocorrelation times of estimators, providing an effective speed up ofthe simulation.

Reduction of Autocorrelation Times in Lattice Path Integral Quantum Monte Carlo via Direct Sampling of the Truncated Exponential Distribution