Fermionic Free Energies from Ab Initio Path Integral Monte Carlo Simulations of Fictitious Identical Particles

We combine the recent η-ensemble path integral Monte Carlo approach to the free energy [Dornheim et al. <i>Phys. Rev. B</i> <b>2025</b> <i>111</i>, L041114] with a recent fictitious partition function technique based on inserting a continuous variable that interpolates between the bosonic and Fermionic limits [Xiong and Xiong <i>J. Chem. Phys.</i> <b>2022</b> <i>157</i>, 094112] to deal with the Fermion sign problem. As a practical example, we apply our setup 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 et al. [<i>Phys. Rev. Lett.</i> <b>2017</b> <i>119</i>, 135001]. 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, and for Fermionic free energy calculations with unprecedented system size.