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arXiv · 0906.4354

A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations

Phani K. V. V. Nukala·P. R. C. Kent
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Abstract

We present an efficient low-rank updating algorithm for updating the trial wavefunctions 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 k-th step compared with traditional algorithms that require O(N^2) computations, where N is the system size. For single determinant trial wavefunctions the new algorithm is faster than the traditional O(N^2) Sherman-Morrison algorithm for up to O(N) updates. For multideterminant configuration-interaction type trial wavefunctions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN^2) work and O(MN^2) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration interaction type wavefunctions.

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Phani K. V. V. Nukala, P. R. C. Kent. 2009-06-23. A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations. https://doi.org/10.1063/1.3142703

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