Exciting Determinants in Quantum Monte Carlo: Loading the Dice with Fast, Low-Memory Weights.

Area of Science:

• Quantum Chemistry
• Computational Physics
• Materials Science

Background:

• Coupled cluster Monte Carlo (CCMC) and full configuration interaction Quantum Monte Carlo (FCIQMC) calculations require high-quality excitation generators for efficiency.
• Existing methods like heat bath sampling (Holmes et al.) offer high efficiency but suffer from prohibitive memory scaling (quartic with system size).
• On-the-fly weight approximation (Alavi et al.) reduces memory but has linear computational scaling with system size.

Purpose of the Study:

• To develop a novel spawn-sampling algorithm that combines the strengths of existing methods.
• To reduce memory requirements and improve computational scaling for CCMC and FCIQMC calculations.
• To provide an efficient excitation generator suitable for large systems and localized orbitals.

Main Methods:

• A new spawn-sampling algorithm is introduced, integrating ideas from heat bath sampling and on-the-fly weight approximation.
• The algorithm leverages the single-reference nature of many systems and is optimized for localized orbitals.
• The method's memory requirements scale quadratically with basis set size, and computational scaling is independent of system size (CCMC) or linear with electron number (FCIQMC).

Main Results:

• The new algorithm demonstrates low memory requirements, significantly better than the heat bath algorithm.
• For larger systems, calculations using the new algorithm converge faster than the on-the-fly weight algorithm.
• Tests on water chains with CCMC and FCIQMC show comparable efficiency to existing excitation generators.

Conclusions:

• The developed spawn-sampling algorithm offers a favorable balance of memory and computational efficiency for CCMC and FCIQMC.
• This method is particularly advantageous for large systems where memory constraints are critical.
• The algorithm represents a significant improvement for quantum Monte Carlo calculations, enabling studies of larger and more complex systems.