We present a fully detailed and highly performing implementation of the Linear Method [J. Toulouse and C. J. Umrigar (2007)] to optimize Jastrow-Feenberg and Backflow Correlations in many-body wave-functions, which are widely used in condensed matter
physics. We show that it is possible to implement such optimization scheme performing analytical derivatives of the wave-function with respect to the variational parameters achieving the best possible complexity O(N^3) in the number of particles N.
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-ro
ton 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.
Defects are believed to play a fundamental role in the supersolid state of 4He. We report on studies by exact Quantum Monte Carlo (QMC) simulations at zero temperature of the properties of solid 4He in presence of many vacancies, up to 30 in two dime
nsions (2D). In all studied cases the crystalline order is stable at least as long as the concentration of vacancies is below 2.5%. In the 2D system for a small number, n_v, of vacancies such defects can be identified in the crystalline lattice and are strongly correlated with an attractive interaction. On the contrary when n_v~10 vacancies in the relaxed system disappear and in their place one finds dislocations and a revival of the Bose-Einstein condensation. Thus, should zero-point motion defects be present in solid 4He, such defects would be dislocations and not vacancies, at least in 2D. In order to avoid using periodic boundary conditions we have studied the exact ground state of solid 4He confined in a circular region by an external potential. We find that defects tend to be localized in an interfacial region of width of about 15 A. Our computation allows to put as upper bound limit to zero--point defects the concentration 0.003 in the 2D system close to melting density.
