  We investigate the quantum phase diagram of Bose-Fermi mixtures of ultracold
dipolar particles trapped in one-dimensional optical lattices in the
thermodynamic limit. With the presence of nearest-neighbor (N.N.) interactions,
a long-ranged ordered crystalline phase (Bose-Fermi solid) is found stabilized
between a Mott insulator of bosons and a band-insulator of fermions in the
limit of weak inter-site tunneling ($J$). When $J$ is increased, such a
Bose-Fermi solid can be quantum melted into a Bose-Fermi liquid through either
a two-stage or a three-stage transition, depending on whether the crystalline
order is dominated by the N.N. interaction between fermions or bosons. These
properties can be understood as quantum competition between a pseudo-spin
frustration and a pseudo-spin-charge separation, qualitatively different from
the classical picture of solid-liquid phase transition.
