Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead.

Area of Science:

• Computational Chemistry
• Quantum Mechanics
• Materials Science

Background:

• The phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method is a powerful tool for electronic structure calculations.
• Standard ph-AFQMC implementations face challenges with computational scaling and memory requirements for large systems.
• Efficient local energy evaluation is crucial for mitigating these challenges.

Purpose of the Study:

• To investigate the integration of the stochastic resolution-of-the-identity (sRI) approximation with ph-AFQMC.
• To evaluate the impact of sRI on the computational scaling and memory footprint of different local energy evaluation strategies within ph-AFQMC.
• To assess the performance of these combined methods for realistic chemical systems.

Main Methods:

• The study combines sRI with four established local energy evaluation techniques: half-rotated (HR), Cholesky decomposition (CD), tensor hypercontraction (THC), and low-rank factorization (LR).
• Numerical calculations were performed on one-dimensional hydrogen chains and water clusters.
• A variance reduction technique was employed in conjunction with CD-sRI.

Main Results:

• HR-sRI showed no scaling improvement. CD-sRI achieved cubic scaling (O(N^3)) for computation and reduced memory to O(N^2).
• THC-sRI and LR-sRI demonstrated quadratic scaling (O(N^2)) for both computation and memory, though potentially with larger prefactors.
• CD-sRI, with variance reduction, achieved cubic scaling without significant overhead, outperforming standard CD (O(N^3-4)) with reduced scaling to O(N^2-3).

Conclusions:

• The integration of sRI with ph-AFQMC offers significant computational advantages, particularly for large systems.
• THC-sRI and LR-sRI are promising for memory-intensive calculations due to their quadratic scaling.
• This work paves the way for more feasible large-scale ph-AFQMC applications, overcoming previous resource limitations.