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

TL;DR

This paper uses advanced path integral Monte Carlo simulations to study the structural and dynamic properties of liquid helium-3 without fixed nodes, providing new insights into Fermi statistics effects and matching experimental data.

Contribution

It introduces ab initio PIMC simulations of liquid $^3$He without nodal constraints, enabling detailed analysis of Fermi statistics effects on structural and dynamic properties.

Findings

Successful reconstruction of dynamic structure factor $S(q,\omega)$ with phonon-maxon-roton dispersion

Excellent agreement between simulation results and neutron scattering experiments

Quantitative assessment of temperature effects on structural properties

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.