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

TL;DR

This paper investigates the fermion sign problem in continuum quantum Monte Carlo methods, showing its exponential decay with system size and imaginary time, and links localization to the severity of the problem.

Contribution

It provides an analytical expression connecting system localization to the sign problem and discusses computational complexity and mitigation strategies.

Findings

Sign problem efficiency decays exponentially with particle number and imaginary time.

Derived an analytical relation between localization and sign problem magnitude.

Numerical results support the analytical predictions.

Abstract

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