Quantum simulation of 3He impurities and of 4He interstitials in solid 4He

We have studied the role of an atomic He-3 impurity and an interstitial He-4 atom in two-dimensional (2D) and three-dimensional (3D) solid He-4 using path-integral Monte Carlo simulation. We find that when a substitutional He-3 impurity is introduced, the impurity becomes localized and occupies an ideal lattice site. When an interstitial He-3 impurity is introduced in the He-4 solid, we find that the impurity becomes localized at a substitutional position and, thus, promotes the extra He-4 atom to the interstitial space. As a consequence we find that the one-body density matrix (OBDM) and the superfluid fraction, for the case of a He-4 solid with an interstitial impurity, are very similar to those calculated for a He-4 solid with a He-4 interstitial atom. Namely, while the off-diagonal OBDM approaches zero exponentially with increasing particle displacement for the "pure" solid, an interstitial He-4 atom or a He-3 impurity appear to enhance it at long distances. Finally, the effective mass of the He-3 impurity quasiparticle in 2D and 3D crystalline He-4 is estimated.