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Accurate thermodynamic simulations of correlated fermions using path integralMonte Carlo (PIMC) methods are of paramount importance for many applicationssuch as the description of ultracold atoms, electrons in quantum dots, andwarm-dense matter. The main obstacle is the fermion sign problem (FSP), whichleads to an exponential increase in computation time both with increasing thesystem-size and with decreasing temperature. Very recently, Hirshberg et al.[J. Chem. Phys. 152, 171102 (2020)] have proposed to alleviate the FSP based onthe Bogoliubov inequality. In the present work, we extend this approach byadding a parameter that controls the perturbation, allowing for anextrapolation to the exact result. In this way, we can also use thermodynamicintegration to obtain an improved estimate of the fermionic energy. As a testsystem, we choose electrons in 2D and 3D quantum dots and find in some cases aspeed-up exceeding 10^6 , as compared to standard PIMC, while retaining arelative accuracy of $\sim0.1\%$. Our approach is quite general and can readilybe adapted to other simulation methods.

Attenuating the fermion sign problem in path integral Monte Carlo simulations using the Bogoliubov inequality and thermodynamic integration