  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.
