  The problem of interacting bosons in frustrated lattices is an intricate one
due to the absence of a unique minimum in the single-particle dispersion where
macroscopic number of bosons can condense. Here we consider a family of
tight-binding models with macroscopically degenerate lowest energy band,
separated from other bands by a gap. We predict the formation of exotic states
that spontaneously break rotational symmetry at relatively low filling. These
states belong to three nematic phases: Wigner crystal, supersolid, and
superfluid. The Wigner crystal phase is established exactly at low filling.
Supersolid and superfluid phases, at larger filling, are obtained by making use
of a projection onto the flat band, construction of an appropriate Wannier
basis, and subsequent mean-field treatment. The nematic superfluid that we
predict is uniform in real space but has an anisotropic momentum distribution,
providing a novel scenario for Bose condensation with an additional nematic
order. Our findings open up a promising direction of studying microscopic
quantum liquid crystalline phases of bosons.
