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 $mathcal{O}(k N)$ 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.