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

We combine the recent $\eta -$ensemble path integral Monte Carlo (PIMC) approach to the free energy [T.~Dornheim $\mathit{\text{et}}\mathit{\text{al.}}$, $\mathit{\text{Phys.}}\mathit{\text{Rev.}}\mathit{\text{B}}$ $\mathbf{\text{111}}$, 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, $\mathit{\text{J.}}\mathit{\text{Chem.}}\mathit{\text{Phys.}}$~$\mathbf{\text{157}}$, 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 $\mathit{\text{et}}\mathit{\text{al.}}$~[$\mathit{\text{Phys.}}\mathit{\text{Rev.}}\mathit{\text{Lett.}}$~$\mathbf{\text{119}}$, 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.