Path integral Monte Carlo approach to the structural properties and collective excitations of liquid [Formula: see text] without fixed nodes

Due to its nature as a strongly correlated quantum liquid, ultracold helium is characterized by the nontrivial interplay of different physical effects. Bosonic [Formula: see text] exhibits superfluidity and Bose-Einstein condensation. Its physical properties have been accurately determined on the basis of ab initio path integral Monte Carlo (PIMC) simulations. In contrast, the corresponding theoretical description of fermionic [Formula: see text] is severely hampered by the notorious fermion sign problem, and previous PIMC results have been derived by introducing the uncontrolled fixed-node approximation. In this work, we present extensive new PIMC simulations of normal liquid [Formula: see text] without any nodal constraints. This allows us to to unambiguously quantify the impact of Fermi statistics and to study the effects of temperature on different physical properties like the static structure factor [Formula: see text] , the momentum distribution [Formula: see text] , and the static density response function [Formula: see text] . In addition, the dynamic structure factor [Formula: see text] is rigorously reconstructed from imaginary-time PIMC data. From simulations of [Formula: see text] , we derived the familiar phonon–maxon–roton dispersion function that is well-known for [Formula: see text] and has been reported previously for two-dimensional [Formula: see text] films (Nature 483:576–579 (2012)). The comparison of our new results for both [Formula: see text] and [Formula: see text] with neutron scattering measurements reveals an excellent agreement between theory and experiment.