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

Abstract

We present extensive new \emph{ab initio} path integral Monte Carlo (PIMC) simulations of normal liquid ${}^3$He without any nodal constraints. This allows us to study the effects of temperature on different structural properties like the 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, the dynamic structure factor $S(\mathbf{q},\omega )$ is rigorously reconstructed from imaginary-time PIMC data, and we find the familiar phonon-maxon-roton dispersion that is well known from ${}^4$He and has been reported previously for two-dimensional ${}^3$He films [Nature \textbf{483}, 576-579 (2012)]. The comparison of our new results for both $S(\mathbf{q})$ and $S(\mathbf{q},\omega )$ to neutron scattering measurements reveals an excellent agreement between theory and experiment.

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