Improved walker population control for full configuration interaction quantum Monte Carlo

Full configuration interaction quantum Monte Carlo (FCIQMC) is a stochastic approach for finding the ground state of a quantum many-body Hamiltonian. It is based on the dynamical evolution of a walker population in Hilbert space, which samples the ground state configuration vector over many iterations. Here we present a modification of the original protocol for walker population control of Booth et al. [JCP 131, 054106 (2009)] in order to achieve equilibration at a pre-defined average walker number and to avoid walker number overshoots. The dynamics of the walker population is described by a noisy damped harmonic oscillator and controlled by two parameters responsible for damping and forcing, respectively. We demonstrate the features of the new population control procedure such as precise walker number control and fast equilibration, and analyse the effects on the stochastic errors of the shift estimator for the ground-state energy. The improved control of the walker number, and thereby memory consumption, is a desirable feature required for automating FCIQMC calculations and requires minimal modifications to existing code.