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.
