Extending J walking to quantum systems: Applications to atomic clusters

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Abstract
The J-walking (or jump-walking) method is extended to quantum systems by incorporating it into the Fourier path integral Monte Carlo methodology. J walking can greatly reduce systematic errors due to quasiergodicity, or the incomplete sampling of configuration space in Monte Carlo simulations. As in the classical case, quantum J walking uses a jumping scheme to overcome configurational barriers. It couples the usual Metropolis sampling to a distribution generated at a higher temperature where the sampling is sufficiently ergodic. The J-walker distributions used in quantum J walking can be either quantum or classical, with classical distributions having the advantage of lower storage requirements, but the disadvantage of being slightly more computationally intensive and having a more limited useful temperature range. The basic techniques are illustrated first on a simple one-dimensional double well potential based on a quartic polynomial. The suitability of J walking for typical multidimensional quantum Monte Carlo systems is then shown by applying the method to a multiparticle cluster system consisting of rare gas atoms bound by pairwise Lennard-Jones potentials. Different degrees of quantum behavior are considered by examining both argon and neon clusters. Remarkable improvements in the convergence rate for the cluster energy and heat capacity, analogous to those found in classical systems, are found for temperatures near the cluster transition regions.