A Pseudo-Fermion Propagator Approach to the Fermion Sign Problem

TL;DR

This paper introduces a pseudo-fermion propagator within path integral Monte Carlo to mitigate the fermion sign problem, enabling accurate and efficient simulations of fermionic systems across different regimes.

Contribution

It presents a novel pseudo-fermion propagator that replaces the fermionic determinant with its absolute value, facilitating sign-problem-free simulations.

Findings

Accurately infers fermionic energies from strongly to weakly degenerate regimes.

Achieves excellent agreement with benchmark results for quantum dots.

Enables efficient first-principles simulations of fermionic systems.

Abstract

In this work, within the framework of path integral Monte Carlo, we construct a pseudo-fermion propagator by replacing the original fermionic determinant with its absolute value. This modified propagator defines an auxiliary system free from the fermion sign problem, enabling efficient simulations of fermionic systems. We found that by shifting the pseudo-fermion energy based on the energy of a non-interacting fermion system, we can efficiently and reliably infer the energy of fermionic systems in various situations, from strong quantum degeneracy to weak quantum degeneracy. We have performed first-principles simulations of quantum dots confined in a two-dimensional harmonic potential and found excellent agreement with benchmark results provided by other established methods. We believe that this pseudo-fermion propagator framework opens up new possibilities for first-principles simulations of fermionic systems.