Population size bias in Diffusion Monte Carlo

Abstract

The size of the population of random walkers required to obtain converged estimates in DMC increases dramatically with system size. We illustrate this by comparing ground state energies of small clusters of parahydrogen (up to 48 molecules) computed by Diffusion Monte Carlo (DMC) and Path Integral Ground State (PIGS) techniques. We contend that the bias associated to a finite population of walkers is the most likely cause of quantitative numerical discrepancies between PIGS and DMC energy estimates reported in the literature, for this few-body Bose system. We discuss the viability of DMC as a general-purpose ground state technique, and argue that PIGS, and even finite temperature methods, enjoy more favorable scaling, and are therefore a superior option for systems of large size.

Seven pages, four figures

References in corpus (6)

• Superfluidity and Quantum Melting of para-Hydrogen clusters
• Structure, superfluidity, and quantum melting of hydrogen clusters
• Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
• Exact ground state Monte Carlo method for Bosons without importance sampling
• A diffusion Monte Carlo study of small para-Hydrogen clusters
• Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme