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The \emph{ab initio} path integral Monte Carlo (PIMC) method is one of themost successful methods in statistical physics, quantum chemistry and relatedfields, but its application to quantum degenerate Fermi systems is severelyhampered by an exponential computational bottleneck: the notorious fermion signproblem. Very recently, Xiong and Xiong [J. Chem. Phys. 157, 094112 (2022)]have suggested to partially circumvent the sign problem by carrying out PIMCsimulations of fictitious systems which contain an interpolating continuousvariable $\xi\in[-1,1]$ in their partition function, with the physical Fermi-and Bose-statistics corresponding to the endpoint limits $\xi=-1$ and $\xi=1$.It has been proposed that thermodynamic information about the fermionic limitmight be obtained by path integral calculations within the bosonic sector$\xi>0$ combined with a quadratic $\xi$ extrapolation throughout the fermionicsector $\xi<0$, essentially bypassing the sign problem. In this work, we showhow the inclusion of the artificial parameter $\xi$ can be interpreted as aneffective penalty on the formation of permutation cycles in the PIMCsimulation. We empirically demonstrate that the proposed extrapolation methodbreaks down for moderate to high quantum degeneracy. Instead, the methodconstitutes a valuable tool for the description of large Fermi-systems of weakquantum degeneracy. This is demonstrated for electrons in a 2D harmonic trapand for the archetypal uniform electron gas (UEG), where we find excellentagreement ($\sim0.5\%$) with exact configuration PIMC results in thehigh-density regime while attaining a speed-up exceeding eleven orders ofmagnitude. Finally, we extend the idea beyond the energy and analyze the radialdensity distribution (2D trap), as well as the static structure factor andimaginary-time density-density correlation function (UEG).

Fermionic physics from ab initio path integral Monte Carlo simulations of fictitious identical particles