Exciting determinants in Quantum Monte Carlo: Loading the dice with fast, low memory weights

TL;DR

This paper introduces a new excitation generator for Quantum Monte Carlo methods that combines efficiency and low memory usage, outperforming existing algorithms in larger systems.

Contribution

It develops a spawn-sampling algorithm with quadratic memory scaling, improving efficiency and scalability over previous heat bath and on-the-fly weight algorithms.

Findings

Comparable efficiency to existing methods on small water chains

Faster convergence for larger systems

Significantly reduced memory requirements

Abstract

High-quality excitation generators are crucial to the effectiveness of Coupled cluster Monte Carlo (CCMC) and full configuration interaction Quantum Monte Carlo (FCIQMC) calculations. The heat bath sampling of Holmes et al. [A. A. Holmes, H. J. Changlani, and C. J. Umrigar, J. Chem. Theory Comput. 12, 1561 (2016)] dramatically increases the efficiency of the spawn step of such algorithms but requires memory storage scaling quartically with system size which can be prohibitive for large systems. Alavi et al. [S. D. Smart, G. H. Booth, and A. Alavi, unpublished] then approximated these weights with weights based on Cauchy--Schwarz-like inequalities calculated on-the-fly. While reducing the memory cost, this algorithm scales linearly in system size computationally. We combine both these ideas with the single reference nature of many systems, and introduce a spawn-sampling algorithm that has low memory requirements (quadratic in basis set size) compared to the heat bath algorithm and only scales either independently of system size (CCMC) or linearly in the number of electrons (FCIQMC). On small water chains with localized orbitals, we show that it is equally efficient as the other excitation generators. As the system gets larger, it converges faster than the on-the-fly weight algorithm, while having a much more favourable memory scaling than the heat bath algorithm.