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

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

2012-01-23

arxiv.org/abs/1201.4691v1

Physics

Computational Physics

16 pages, 22 figures

Scientific paper

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 $0.5 \leq r_s \leq 5.0$ 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, and this can be justified on physical grounds. We expect the fixed shift strategy to greatly reduce the computational cost of many i-FCIQMC calculations. In addition, we provide benchmarks for the electron gas, to be used by other quantum chemical methods in exploring periodic solid state systems.

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