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

TL;DR

This paper introduces a low-rank updating algorithm for Slater determinants in Quantum Monte Carlo simulations, significantly reducing computational complexity and enabling more accurate, efficient calculations with complex trial wavefunctions.

Contribution

The paper presents a novel low-rank updating algorithm that improves efficiency for updating Slater determinants in QMC, outperforming traditional methods especially for multi-determinant wavefunctions.

Findings

Reduced computational complexity to O(kN) per update

Faster than Sherman-Morrison for up to O(N) updates

Enables more accurate and efficient QMC with multi-determinant wavefunctions

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.