  We investigate the phases of a Bose-Einstein condensate of dipolar atoms
restricted to move in a two-dimensional plane. The dipole moments are all
aligned in a direction tilted with respect to the plane normal. As a result of
the attractive and repulsive components of the dipole-dipole interaction, the
dipolar gas has a self-bound phase, which is stabilized by quantum
fluctuations. Furthermore, tilting the dipoles tunes the anisotropy of the
dipole-dipole interaction, which can trigger a spatial density modulation. In
this work we study these two aspects and investigate the conditions for the
formation of a self-bound and striped phase, which has been realized in
experiments with dipolar droplets. We use a variational method based on the
hypernetted-chain Euler-Lagrange optimization of a Jastrow-Feenberg ansatz for
the many-body wave function to study the ground state properties. This method
takes into account quantum fluctuations in a non-perturbative way and thus can
be used also for strongly correlated systems.
