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

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(N-2) computations, where N is the system size. For single determinant trial wave functions 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 wave functions of M+1 determinants, the new algorithm is significantly more efficient, saving both O(MN2) work and O(MN2) storage. The algorithm enables more accurate and significantly more efficient QMC calculations using configuration-interaction-type wave functions.