Stochastic resolution-of-the-identity auxiliary-field quantum Monte Carlo: Scaling reduction without overhead.
J Chem Phys
; 153(4): 044131, 2020 Jul 28.
Article
en En
| MEDLINE
| ID: mdl-32752714
ABSTRACT
We explore the use of the stochastic resolution-of-the-identity (sRI) with the phaseless auxiliary-field quantum Monte Carlo (ph-AFQMC) method. sRI is combined with four existing local energy evaluation strategies in ph-AFQMC, namely, (1) the half-rotated electron repulsion integral tensor (HR), (2) Cholesky decomposition (CD), (3) tensor hypercontraction (THC), or (4) low-rank factorization (LR). We demonstrate that HR-sRI achieves no scaling reduction, CD-sRI scales as O(N3), and THC-sRI and LR-sRI scale as O(N2), albeit with a potentially large prefactor. Furthermore, the walker-specific extra memory requirement in CD is reduced from O(N3) to O(N2) with sRI, while sRI-based THC and LR algorithms lead to a reduction from O(N2) extra memory to O(N). Based on numerical results for one-dimensional hydrogen chains and water clusters, we demonstrated that, along with the use of a variance reduction technique, CD-sRI achieves cubic-scaling without overhead. In particular, we find that for the systems studied, the observed scaling of standard CD is O(N3-4), while for CD-sRI, it is reduced to O(N2-3). Once a memory bottleneck is reached, we expect THC-sRI and LR-sRI to be preferred methods due to their quadratic-scaling memory requirements and their quadratic-scaling of the local energy evaluation (with a potentially large prefactor). The theoretical framework developed here should facilitate large-scale ph-AFQMC applications that were previously difficult or impossible to carry out with standard computational resources.
Texto completo:
1
Banco de datos:
MEDLINE
Idioma:
En
Revista:
J Chem Phys
Año:
2020
Tipo del documento:
Article
País de afiliación:
Estados Unidos