2008/01/08 by J. R. Trail · 1 citation
Materials Science · Mathematics · Physics and Astronomy · #Advanced Chemical Physics Studies #Applied mathematics #Central limit theorem #Dynamic Monte Carlo method #Hybrid Monte Carlo #Machine Learning in Materials Science #Markov chain Monte Carlo #Mathematics #Monte Carlo integration #Monte Carlo method #Monte Carlo method in statistical physics #Monte Carlo molecular modeling #Physics #Quantum Monte Carlo #Quantum, superfluid, helium dynamics #Quasi-Monte Carlo method #Statistical physics #Statistics #Variational Monte Carlo #cond-mat.stat-mech #physics.comp-ph #quant-ph
paper · pdf · doi:10.1103/physreve.77.016704
published as Phys. Rev. E 77, 016704 (2008) · 14 pages, 9 figures
openalex publication_date 2008/01/08 · arxiv created 2009/09/30 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05
Expectation values of physical quantities may accurately be obtained by the evaluation of integrals within many-body quantum mechanics, and these multidimensional integrals may be estimated using Monte Carlo methods. In a previous publication it has been shown that for the simplest, most commonly applied strategy in continuum quantum Monte Carlo, the random error in the resulting estimates is not well controlled. At best the central limit theorem is valid in its weakest form, and at worst it is invalid and replaced by an alternative generalized central limit theorem and non-normal random error. In both cases the random error is not controlled. Here we consider a new "residual sampling strategy" that reintroduces the central limit theorem in its strongest form, and provides full control of the random error in estimates. Estimates of the total energy and the variance of the local energy within variational Monte Carlo are considered in detail, and the approach presented may be generalized to expectation values of other operators, and to other variants of the quantum Monte Carlo method.