  We predict that ultracold bosonic dipolar gases, confined within a multilayer
geometry, may undergo self-assembling processes, leading to the formation of
chain gases and solids. These dipolar chains, with dipoles aligned across
different layers, emerge at low densities and resemble phases observed in
liquid crystals, such as nematic and smectic phases. We calculate the phase
diagram using quantum Monte Carlo methods, introducing a newly devised trial
wave function designed for describing the chain gas, where dipoles from
different layers form chains without in-plane long-range order. We find gas,
solid, and chain phases, along with quantum phase transitions between these
states. Specifically, we predict a quantum phase transition from a gaseous to a
self-ordered phase, which occurs at a critical interlayer distance. Remarkably,
in the self-organized phases, the mean interparticle distance can significantly
exceed the characteristic length of the interaction potential, yielding solids
and chain gases with densities several orders of magnitude lower than those of
conventional quantum solids.
