A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations

Phani K.V.V. Nukala; P. R.C. Kent

doi:10.1063/1.3142703

A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations

Phani K.V.V. Nukala, P. R.C. Kent

Computational Chemistry and Nanomaterial

Research output: Contribution to journal › Article › peer-review

24 Scopus citations

Abstract

We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O (kN) during the kth step compared to traditional algorithms that require O (N²) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O (N²) Sherman-Morrison algorithm for up to O (N) updates. For multideterminant configuration- interaction-type trial wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O (M N²) work and O (M N²) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.

Original language	English
Article number	204105
Journal	Journal of Chemical Physics
Volume	130
Issue number	20
DOIs	https://doi.org/10.1063/1.3142703
State	Published - 2009

Funding

P.R.C.K. wishes to thank F. A. Reboredo, J. Kim, and R. Q. Hood for helpful conversations. This research was sponsored by the Mathematical, Information and Computational Sciences Division, Office of Advanced Scientific Computing Research and the Center for Nanophase Materials Sciences, Office of Basic Energy Sciences, both of the U.S. Department of Energy and under Contract No. DE-AC05-00OR22725 with UT-Battelle, LLC. The QMC Endstation project is supported by the U.S. Department of Energy (DOE) under Contract No. DOE-DE-FG05-08OR23336.

Funders	Funder number
Center for Nanophase Materials Sciences
U.S. Department of Energy	DE-AC05-00OR22725, DOE-DE-FG05-08OR23336
Basic Energy Sciences
Advanced Scientific Computing Research

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abstract = "We present an efficient low-rank updating algorithm for updating the trial wave functions used in quantum Monte Carlo (QMC) simulations. The algorithm is based on low-rank updating of the Slater determinants. In particular, the computational complexity of the algorithm is O (kN) during the kth step compared to traditional algorithms that require O (N2) computations, where N is the system size. For single determinant trial wave functions the new algorithm is faster than the traditional O (N2) Sherman-Morrison algorithm for up to O (N) updates. For multideterminant configuration- interaction-type trial wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O (M N2) work and O (M N2) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.",

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A fast and efficient algorithm for Slater determinant updates in quantum Monte Carlo simulations

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