Emergence of Critical Phenomena in Full Configuration Interaction Quantum Monte Carlo

There has been recent literature discussion on the origin and severity of the sign problem' in full configuration interaction quantum Monte Carlo (FCIQMC) and its initiator’ adaptation (i-FCIQMC), methods of interest and potential because they allow for exact (FCI) ground-state solutions to be obtained often at a much reduced computational cost. In this study we aim to use a simple order parameter, describing the `sign structure’ of the stochastic wavefunction representation, to empirically characterise the fundamentally different collective behaviour of the walker population in both methods.