Investigation of the Full Configuration Interaction Quantum Monte Carlo Method Using Homogeneous Electron Gas Models

Abstract

Using the homogeneous electron gas (HEG) as a model, we investigate the sources of error in the `initiator' adaptation to Full Configuration Interaction Quantum Monte Carlo (i-FCIQMC), with a view to accelerating convergence. In particular we find that the fixed shift phase, where the walker number is allowed to grow slowly, can be used to effectively assess stochastic and initiator error. Using this approach we provide simple explanations for the internal parameters of an i-FCIQMC simulation. We exploit the consistent basis sets and adjustable correlation strength of the HEG to analyze properties of the algorithm, and present finite basis benchmark energies for N=14 over a range of densities $0.5\le r_s\le 5.0$ a.u. A \emph{single-point extrapolation} scheme is introduced to produce complete basis energies for 14, 38 and 54 electrons. It is empirically found that, in the weakly correlated regime, the computational cost scales linearly with the plane wave basis set size, which is justifiable on physical grounds. We expect the fixed shift strategy to reduce the computational cost of many \iFCIQMC calculations of weakly correlated systems. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

16 pages, 22 figures

References in corpus (6)

• Inhomogeneous backflow transformations in quantum Monte Carlo calculations
• Phase Diagram of the Low-Density Two-Dimensional Homogeneous Electron Gas
• A Full Configuration Interaction Perspective on the Homogeneous Electron Gas
• Convergence of many-body wavefunction expansions using a plane wave basis: from the homogeneous electron gas to the solid state
• Finite-size correction in many-body electronic structure calculations
• The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

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