Massimo Boninsegni

Detailed numerical results obtained with state-of-the-art Quantum Monte Carlo (QMC) simulations are presented for the superfluid phase of ⁴ He at saturated vapor pressure. The aim of this contribution is that of providing reliable, up-to-date estimates for this archetypal superfluid, reflecting the methodological progress that has taken place over the past two decades. We simulate a system comprising 2,048 helium atoms, i.e., an order of magnitude greater in size than those for which results currently regarded as standard references were originally obtained. We offer revised estimates for energetic and structural properties, as well as for the ground state condensate fraction.

Computer simulations yield evidence of superfluid behavior of nanoscale size clusters of parahydrogen adsorbed on a graphite substrate at low temperature (T ≲ 0.25 K). Clusters with a number of molecules between 7 and 12 display concurrent superfluidity and crystalline order, reflecting the corrugation of the substrate. Remarkably, it is found that specific clusters with a number of molecules ranging between 7 and 12 self-diffuse on the surface like free particles, despite the strong pinning effect of the substrate. This effect is underlain by coordinated quantum-mechanical exchanges of groups of identical molecules; that is, it has no classical counterpart.

The one-particle density matrix of a one-dimensional system of fermions featuring a hard core repulsive interaction at short distances can be computed (numerically) exactly by means of the continuous-space Worm Algorithm, without any sign instability. We present here the results for this quantity, and the related momentum distribution, for a ³He fluid. It is shown that the effects of quantum statistics are observable in the fully polarized system, and are progressively suppressed as the polarization approaches zero, as atoms become essentially distinguishable.

The superfluid response of nanoscale size quasi-2D 4He droplets adsorbed on a graphite substrate is investigated by computer simulations. It is found that clusters comprising as few as 7 atoms are stable at temperatures of ≲0.15 K. Clusters of ∼20 atoms or less are liquid-like and ∼100% superfluid. As the size is increased, the central region crystallizes, forming the commensurate C1/3 phase, with a quasi-1D surface layer of superfluidity possibly evolving into a Luttinger liquid or a transverse quantum superfluid with increasing cluster size. The relevance to quasi-2D molecular spectroscopy is discussed.

We investigate mixed (50/50) clusters of parahydrogen and orthodeuterium at low temperatures, by means of quantum Monte Carlo simulations. Our results provide evidence of liquid-like behavior and partial isotopic separation in a cluster of 640 molecules, at temperature T = 10 K. As the temperature is lowered below ∼6 K, crystallization occurs, with no indication that the liquid phase is more resilient at low temperatures in a mixed cluster. Isotopic separation is therefore predicted to take place at low temperatures only through the slow process of molecular self-diffusion in a crystalline matrix.

We revisit the problem of adsorption of a single ⁴He layer on graphene, focusing on the commensurate (C _1/3) crystalline phase, specifically on whether it may possess a nonzero superfluid response, and on the existence of superfluid phases, either (metastable) liquid or vacancy-doped crystalline. We make use of canonical quantum Monte Carlo simulations at zero and finite temperature, based on a realistic microscopic model of the system. Our results confirm the absence of any superfluid response in the commensurate crystal, and that no thermodynamically stable uniform phase exists at lower coverage. No evidence of a possibly long-lived, metastable superfluid phase at C _1/3 coverage is found. Altogether, the results of ground-state projection methods and finite-temperature simulations are entirely consistent.