Excitation spectrum in two-dimensional superfluid 4He

In this work we perform an ab-initio study of an ideal two-dimensional sample of 4He atoms, a model for 4He films adsorbed on several kinds of substrates. Starting from a realistic hamiltonian we face the microscopic study of the excitation phonon-roton spectrum of the system at zero temperature. Our approach relies on Path Integral Ground State Monte Carlo projection methods, allowing to evaluate exactly the dynamical density correlation functions in imaginary time, and this gives access to the dynamical structure factor of the system S(q,omega), containing information about the excitation spectrum E(q), resulting in sharp peaks in S(q,omega). The actual evaluation of S(q,omega) requires the inversion of the Laplace transform in ill-posed conditions, which we face via the Genetic Inversion via Falsification of Theories technique. We explore the full density range from the region of spinodal decomposition to the freezing density, i.e. 0.0321 A^-2 - 0.0658 A^-2. In particular we follow the density dependence of the excitation spectrum, focusing on the low wave--vector behavior of E(q), the roton dispersion, the strength of single quasi--particle peak, Z(q), and the static density response function, chi(q). As the density increases, the dispersion E(q) at low wave--vector changes from a super-linear (anomalous dispersion) trend to a sub-linear (normal dispersion) one, anticipating the crystallization of the system; at the same time the maxon-roton structure, which is barely visible at low density, becomes well developed at high densities and the roton wave vector has a strong density dependence. Connection is made with recent inelastic neutron scattering results from highly ordered silica nanopores partially filled with 4He.

Microscopic studies of solid 4He with Path Integral Projector Monte Carlo

We have investigated the ground state properties of solid $^4$He with the Shadow Path Integral Ground State method. This exact T=0 K projector method allows to describes quantum solids without introducing any a priori equilibrium position. We have found that the efficiency in computing off-diagonal properties in the solid phase sensibly improves when the direct sampling of permutations, in principle not required, is introduced. We have computed the exact one-body density matrix (obdm) in large commensurate 4He crystal finding a decreasing condensate fraction with increasing imaginary time of projection, making our result not conclusive on the presence of Bose-Einstein condensation in bulk solid 4He. We can only give an upper bound of 2.5 times 10^-8 on the condensate fraction. We have exploited the SPIGS method to study also 4He crystal containing grain boundaries by computing the related surface energy and the obdm along these defects. We have found that also highly symmetrical grain boundaries have a finite condensate fraction. We have also derived a route for the estimation of the true equilibrium concentration of vacancies x_v in bulk T=0 K solid 4He, which is shown to be finite, x_v=0.0014(1) at the melting density, when computed with the variational shadow wave function technique.