Fermionic free energies from \textit{ab initio} path integral Monte Carlo simulations of fictitious identical particles

TL;DR

This paper introduces a novel combination of path integral Monte Carlo and fictitious partition function techniques to accurately compute free energies of fermionic systems, demonstrated on the warm dense electron gas.

Contribution

It develops a new method integrating $ extit{ab initio}$ PIMC with a fictitious partition function to address the fermion sign problem in free energy calculations.

Findings

Accurate exchange-correlation free energies for warm dense electron gas.

Excellent agreement with existing parametrizations.

Method applicable to various interacting Fermi-systems.

Abstract

We combine the recent $\eta-$ensemble path integral Monte Carlo (PIMC) approach to the free energy [T.~Dornheim \textit{et al.}, \textit{Phys.~Rev.~B} \textbf{111}, L041114 (2025)] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and fermionic limits [Xiong and Xiong, \textit{J.~Chem.~Phys.}~\textbf{157}, 094112 (2022)] to deal with the fermion sign problem. As a practical example, we apply our set-up to the warm dense uniform electron gas over a broad range of densities and temperatures. We obtain accurate results for the exchange--correlation free energy down to half the Fermi temperature, and find excellent agreement with the state-of-the-art parametrization by Groth \textit{et al.}~[\textit{Phys.~Rev.~Lett.}~\textbf{119}, 135001 (2017)]. Our work opens up new avenues for the future study of a host of interacting Fermi-systems, including warm dense matter, ultracold atoms, and electrons in quantum dots.