A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations
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.
Cite
@article{arxiv.0906.4354,
title = {A Fast and Efficient Algorithm for Slater Determinant Updates in Quantum Monte Carlo Simulations},
author = {Phani K. V. V. Nukala and P. R. C. Kent},
journal= {arXiv preprint arXiv:0906.4354},
year = {2009}
}