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

TL;DR

This paper evaluates the Full Configuration Interaction Quantum Monte Carlo method using homogeneous electron gas models, introduces a single-point extrapolation scheme, and analyzes error sources to improve convergence and computational efficiency.

Contribution

It provides a detailed analysis of error sources in i-FCIQMC, introduces a new extrapolation scheme for basis energies, and benchmarks the method for various electron counts and densities.

Findings

Fixed shift phase effectively assesses stochastic and initiator errors.

Computational cost scales linearly with basis set size in weakly correlated regimes.

Benchmarks for N=14, 38, 54 electrons across different densities are provided.

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 $0.5 \leq r_s \leq 5.0$ 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, 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.