Quantum Monte Carlo Simulations with RANLUX Random Number Generator

We estimate the ground state energy of the hydrogen atom using the variational Monte Carlo (VMC) method with a simple model trial wavefunction and the RANLUX random number generator with five luxury levels (RANLUX-[04]). The resulting VMC energies are compared with the reference (exact) energy that is analytically evaluated with the same wavefunction as in the VMC simulations. The VMC energies with RANLUX-[1-4] are in good agreement with the reference energy within their statistical errors. On the other hand, RANLUX-0 with the lowest luxury level is found to give a systematic error of about 0.2 mhartree. In addition, we examine the time-step dependence of statistical quantities in VMC simulations. We find that the error bar of the VMC energy and the correlation time in VMC data have a minimum at a 50 % acceptance ratio in the Metropolis procedure.