Quantized vortices in two dimensional solid 4He

TL;DR

This study uses quantum Monte Carlo methods to analyze the properties of quantized vortices in two-dimensional solid helium-4, revealing their static nature and limited impact on lattice and quantum properties under the Onsager-Feynman approximation.

Contribution

It introduces a fixed-phase quantum Monte Carlo approach to model vortices in 2D solid helium-4, showing their static positioning and minimal influence on the crystal's properties.

Findings

Vortex core sits in an interstitial site.

Vortex has little effect on static structure factor and vacancies.

Vortex cannot sustain itself without pre-existing condensate.

Abstract

Diagonal and off-diagonal properties of 2D solid 4He systems doped with a quantized vortex have been investigated via the Shadow Path Integral Ground State method using the fixed-phase approach. The chosen approximate phase induces the standard Onsager-Feynman flow field. In this approximation the vortex acts as a static external potential and the resulting Hamiltonian can be treated exactly with Quantum Monte Carlo methods. The vortex core is found to sit in an interstitial site and a very weak relaxation of the lattice positions away from the vortex core position has been observed. Also other properties like Bragg peaks in the static structure factor or the behavior of vacancies are very little affected by the presence of the vortex. We have computed also the one-body density matrix in perfect and defected 4He crystals finding that the vortex has no sensible effect on the off-diagonal long range tail of the density matrix. Within the assumed Onsager Feynman phase, we find that a quantized vortex cannot auto-sustain itself unless a condensate is already present like when dislocations are present. It remains to be investigated if backflow can change this conclusion.