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We use the Shadow Wave Function formalism as a convenient model to study thefermion sign problem affecting all projector Quantum Monte Carlo methods incontinuum space. We demonstrate that the efficiency of imaginary timeprojection algorithms decays exponentially with increasing number of particlesand/or imaginary-time propagation. Moreover, we derive an analytical expressionthat connects the localization of the system with the magnitude of the signproblem, illustrating this prediction through some numerical results. Finally,we discuss the fermion sign problem computational complexity and methods foralleviating its severity.

On the Fermion Sign Problem in Imaginary-Time Projection Continuum Quantum Monte Carlo with Local Interaction