Microscopic calculation of the phonon-roton branch in superfluid $^4$He

TL;DR

This paper uses advanced Monte Carlo methods to accurately calculate the phonon-roton excitation spectrum in superfluid helium-4, achieving results that closely match experimental data.

Contribution

It demonstrates the effectiveness of fixed-node and released-node Monte Carlo techniques in precisely modeling excitations in superfluid helium-4.

Findings

Results agree well with experimental data at various densities

Fixed-node bounds become exact with released-node techniques

Method provides reliable excitation energies in superfluid helium-4

Abstract

Diffusion Monte Carlo results for the phonon-roton excitation branch in bulk liquid $^4$He at zero temperature are presented. The sign problem associated to the excited wave function has been dealt both with the fixed-node approximation and the released-node technique. The upper bounds provided by the fixed-node approximation are shown to become exact when using the released-node method. An excellent agreement with experimental data is achieved both at the equilibrium and near the freezing densities.