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We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC)simulations of normal liquid $^3$He without any nodal constraints. This allowsus to study the effects of temperature on different structural properties likethe static structure factor $S(\mathbf{q})$, the momentum distribution$n(\mathbf{q})$, and the static density response function $\chi(\mathbf{q})$,and to unambiguously quantify the impact of Fermi statistics. In addition, thedynamic structure factor $S(\mathbf{q},\omega)$ is rigorously reconstructedfrom imaginary-time PIMC data, and we find the familiar phonon-maxon-rotondispersion that is well known from $^4$He and has been reported previously fortwo-dimensional $^3$He films [Nature \textbf{483}, 576-579 (2012)]. Thecomparison of our new results for both $S(\mathbf{q})$ and$S(\mathbf{q},\omega)$ to neutron scattering measurements reveals an excellentagreement between theory and experiment.

Path Integral Monte Carlo Simulations of liquid $^3$He without Fixed Nodes: Structural Properties and Collective Excitations