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 (13)

• Quantum Monte Carlo Calculations of Light Nuclei
• Superfluidity and Quantum Melting of para-Hydrogen clusters
• Structure, superfluidity, and quantum melting of hydrogen clusters
• Path Integral Ground State with a Fourth-Order Propagator: Application to Condensed Helium
• Kosterlitz-Thouless transition of the quasi two-dimensional trapped Bose gas
• The momentum distribution of the homogeneous electron gas
• Exact ground state Monte Carlo method for Bosons without importance sampling
• Many-body trial wave functions for atomic systems and ground states of small noble gas clusters
• Diffusion Monte Carlo: Exponential scaling of computational cost for large systems
• On the possible "supersolid" character of parahydrogen clusters
• A diffusion Monte Carlo study of small para-Hydrogen clusters
• Reptation quantum Monte Carlo for lattice Hamiltonians with a directed-update scheme
• Solidification of small para-H2 clusters at zero temperature

Cited by in corpus (41)

• Variational and Diffusion Quantum Monte Carlo Calculations with the CASINO Code
• Theory of Finite Size Effects for Electronic Quantum Monte Carlo Calculations of Liquids and Solids
• Microscopic molecular superfluid response: theory and simulations
• A path integral Monte Carlo method for Rényi entanglement entropies
• Phase diagram of ${}^4$He on graphene
• Projective quantum Monte Carlo simulations guided by unrestricted neural network states
• Ground State Phase Diagram of Parahydrogen in One Dimension
• Particle entanglement in continuum many-body systems via quantum Monte Carlo
• Coexistence, interfacial energy, and the fate of microemulsions in 2D dipolar bosons
• Self-learning projective quantum Monte Carlo simulations guided by restricted Boltzmann machines
• Phases of dipolar bosons in a bilayer geometry
• Absence of superfluidity in 2D dipolar Bose striped crystals
• Simulated quantum annealing of double-well and multi-well potentials
• Simulating disordered quantum systems via dense and sparse restricted Boltzmann machines
• Adsorption by design: tuning atom-graphene van der Waals interactions via mechanical strain
• Novel behaviors of monolayer quantum gases on Graphene, Graphane and Fluorographene
• Assessing the Performance of the Diffusion Monte Carlo Method as Applied to the Water Monomer, Dimer, and Hexamer
• First-Principles Modeling of Quantum Nuclear Effects and Atomic Interactions in Solid 4He at High Pressure
• Quasi-2D Liquid He-3
• Speeding up the ab initio diffusion Monte Carlo by a smart lattice regularization
• Absence of superfluidity in a parahydrogen film intercalated within a crystal of Na atoms
• Stochastic differential equation approach to understanding the population control bias in full configuration interaction quantum Monte Carlo
• Tunneling in projective quantum Monte Carlo simulations with guiding wave functions
• Dipolar bosons in one dimension: the case of longitudinal dipole alignment
• Morphology of dipolar Bose droplets
• Low-density phases of ${}^3$He monolayers adsorbed on graphite
• Lattice Bose polarons at strong coupling and quantum criticality
• Stochastic lists: Sampling multi-variable functions with population methods
• Systematics of small parahydrogen clusters in two dimensions
• Zero-temperature Monte Carlo simulations of two-dimensional quantum spin glasses guided by neural network states
• Adsorption of parahydrogen on graphene
• Phase diagram and crystal melting of helium-4 in two dimensions
• Hard core repulsion and supersolid cluster crystals
• Quantum Monte Carlo study of thin parahydrogen films on graphite
• The solid phase of He-4: A Monte Carlo simulation study
• Thin He-4 films on alkali substrates: where do He-3 atoms bind?
• He-4 monolayer on Graphene: a Quantum Monte Carlo study
• Phase diagram of muonium hydride: when dimensionality matters
• Bose one-component plasma in 2D: a Monte Carlo study
• Ground state correlations in the one-dimensional Fermi one-component plasma
• Bound state of a He-3 atom at the interface of crystal and superfluid He-4