  Experiments on quantum degenerate Fermi gases of magnetic atoms and dipolar
molecules begin to probe their broken symmetry phases dominated by the
long-range, anisotropic dipole-dipole interaction. Several candidate phases
including the p-wave superfluid, the stripe density wave, and a supersolid have
been proposed theoretically for two-dimensional spinless dipolar Fermi gases.
Yet the phase boundaries predicted by different approximations vary greatly,
and a definitive phase diagram is still lacking. Here we present a theory that
treats all competing many-body instabilities in the particle-particle and
particle-hole channel on equal footing. We obtain the low temperature phase
diagram by numerically solving the functional renormalization-group flow
equations and find a nontrivial density wave phase at small dipolar tilting
angles and strong interactions, but no evidence of the supersolid phase. We
also estimate the critical temperatures of the ordered phases.
