Matsubara Green's function of 3He atoms floating on a 4He film adsorbed on graphite: A worm algorithm Monte Carlo study with a fictitious potential

A system consisting of He-3 atoms floating on the surface of a He-4 film adsorbed to a graphite substrate is simulated using the state-of-the-art worm algorithm path integral Monte Carlo technique. The He-4-He-4 interactions are described by the usual HFDHE2 potential of Aziz et al. [J. Chem. Phys. 70, 4330 (1979)], whereas the He-3-He-3 interactions are modelled by a fictitious potential (FP) introduced to see what new features can be obtained. We are, so to speak, imagining and predicting the future experimental design of such synthetic potentials based on the fact that before the advent of the Feshbach resonance technique the manipulations of interatomic interactions was unthinkable. This work particularly examines the finite-temperature Matsubara Greeds function (MGF) of the above system, and to the best of knowledge this has not been done before. It is found that the MGF displays strong signals arising from particle-hole (p-h) excitations in the He-3 as well as the He-4 layers. The main goal of this work is then to shed light on the role played by the He-3 atoms in defining the strength of these excitations that are explained to occur as a result of He-4 particle promotions to the He-3 layer and the zero-point motion of He-3 atoms. It is argued, that the scattering of the He-4 atoms with the He-3 particles is the major driving force for strong p-h excitations signalled by the MGF. For some reason, the statistical potential is able to yield values for the numerically obtained zero-point kinetic energy that is close to the one from ideal gas theory. In the absence of He-3 atoms, no strong p-h excitations are detected. Our efforts are aimed at a rejuvination of this subject by an examination of the MGF, as the literature on this topic is rare. A value-added feature of this work is the use of the above mentioned FP for a qualitative description of the He-3-He-3 interactions since we are only interested in a qualitative study. The spatial positions of He-3 and He-4 atoms are displayed in a set of figures, with emphasis on a "fake" He-3 clusterization. Numerical results for the energies are presented which are comparable to those reported by Krotscheck [Phys. Rev. B 32, 5713 (1985)] and Gasparini et al. [Phys. Rev. B 29, 4921 (1984)]. It should be noted, that the present simulations have been heavy-computational and required extensive CPU times.