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The ab initio thermodynamic simulation of correlated Fermi systems is ofcentral importance for many applications, such as warm dense matter, electronsin quantum dots, and ultracold atoms. Unfortunately, path integral Monte Carlo(PIMC) simulations of fermions are severely restricted by the notorious fermionsign problem (FSP). In this work, we present a hands-on discussion of the FSPand investigate in detail its manifestation with respect to temperature, systemsize, interaction-strength and -type, and the dimensionality of the system.Moreover, we analyze the probability distribution of fermionic expectationvalues, which can be non-Gaussian and fat-tailed when the FSP is severe. As apractical application, we consider electrons and dipolar atoms in a harmonicconfinement, and the uniform electron gas in the warm dense matter regime. Inaddition, we provide extensive PIMC data, which can be used as a reference forthe development of new methods and as a benchmark for approximations.

The Fermion Sign Problem in Path Integral Monte Carlo Simulations: Quantum Dots, Ultracold Atoms, and Warm Dense Matter