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

Journal Article · Fri May 01 00:00:00 EDT 2009 · Journal of Chemical Physics

DOI:https://doi.org/10.1063/1.3142703· OSTI ID:1050244

Nukala, Phani K. ^[1]; Kent, Paul R.  ^[1]

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1. ORNL

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

• Research Organization: Oak Ridge National Lab. (ORNL), Oak Ridge, TN (United States)
• Sponsoring Organization: USDOE
• DOE Contract Number: AC05-00OR22725
• OSTI ID: 1050244
• Journal Information: Journal of Chemical Physics, Vol. 130, Issue 20; ISSN 0021-9606
• Country of Publication: United States
• Language: English