Emergence of Critical Phenomena in Full Configuration Interaction Quantum Monte Carlo

TL;DR

This paper investigates the sign problem in FCIQMC and i-FCIQMC methods, using an order parameter to empirically analyze the collective behavior of walkers and the emergence of critical phenomena.

Contribution

It introduces a simple order parameter to characterize the sign structure and collective behavior in FCIQMC and i-FCIQMC, highlighting critical phenomena.

Findings

Identification of phase transition-like behavior in walker populations

Empirical characterization of sign structure dynamics

Insights into the severity of the sign problem

Abstract

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.