Path Integral Calculations of exchange in solid 4He

TL;DR

This paper uses Path Integral Monte Carlo to calculate exchange frequencies in solid 4He, showing that these do not support supersolid behavior, thus constraining possible mechanisms for supersolidity.

Contribution

The study provides the first detailed PIMC calculations of ring exchange frequencies in solid 4He and relates them to the absence of supersolid behavior.

Findings

Exchange frequencies follow a simple lattice model.

Calculated exchange rates do not support supersolid phase.

Long exchange processes are characterized for mass transport.

Abstract

Recently there have been experimental indications that solid 4He might be a supersolid. We discuss the relation of supersolid behavior to ring exchange. The tunnelling frequencies for ring exchanges in quantum solids are calculated using Path Integral Monte Carlo by finding the free energy for making a path that begins with the atoms in one configuration and ends with a permutation of those positions. We find that the exchange frequencies in solid 4He are described by a simple lattice model which does not show supersolid behavior. Thus, the PIMC calculations constrain the mechanism for the supersolid behavior. We also look at the characteristics of very long exchanges needed for macroscopic mass transport.