The sign problem and population dynamics in the full configuration interaction quantum Monte Carlo method

TL;DR

This paper examines the sign problem in the full configuration interaction quantum Monte Carlo method, explaining how particle cancellation ensures convergence and analyzing how the problem's severity varies with different systems.

Contribution

It provides a detailed analysis of the sign problem and population dynamics in the FCIQMC method, enhancing understanding of its convergence properties.

Findings

Sign problem severity depends on the system studied.

Particle cancellation ensures convergence to the ground state.

Population dynamics are characterized by specific stochastic behaviors.

Abstract

The recently proposed full configuration interaction quantum Monte Carlo method allows access to essentially exact ground-state energies of systems of interacting fermions substantially larger than previously tractable without knowledge of the nodal structure of the ground-state wave function. We investigate the nature of the sign problem in this method and how its severity depends on the system studied. We explain how cancelation of the positive and negative particles sampling the wave function ensures convergence to a stochastic representation of the many-fermion ground state and accounts for the characteristic population dynamics observed in simulations.