Fermion Sign Problem in Path Integral Monte Carlo Simulations: Grand-canonical ensemble

TL;DR

This paper analyzes the fermion sign problem in grand-canonical ensemble fermionic path integral Monte Carlo simulations, highlighting its severity compared to canonical ensemble and discussing feasible approaches for certain systems relevant to condensed matter physics.

Contribution

It provides a practical analysis of the fermion sign problem in GCE PIMC, demonstrating its severity and exploring conditions under which simulations remain feasible.

Findings

Sign problem is more severe in GCE than in canonical ensemble.

GCE PIMC simulations are feasible for certain systems despite the sign problem.

Implications for studying warm dense matter, ultracold atoms, and quantum dots.

Abstract

We present a practical analysis of the fermion sign problem in fermionic path integral Monte Carlo (PIMC) simulations in the grand-canonical ensemble (GCE). As a representative model system, we consider electrons in a $2D$ harmonic trap. We find that the sign problem in the GCE is even more severe than in the canonical ensemble at the same conditions, which, in general, makes the latter the preferred option. Despite these difficulties, we show that fermionic PIMC simulations in the GCE are still feasible in many cases, which potentially gives access to important quantities like the compressiblity or the Matsubara Greens function. This has important implications for contemporary fields of research such as warm dense matter, ultracold atoms, and electrons in quantum dots.